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Presentation on the topic "Rectilinear and curvilinear motion. Movement of a body in a circle"

Topic: Curvilinear motion. Uniform movement material point around the circumference.

Lesson objectives: to develop students’ understanding of curvilinear motion, frequency, angular movement, and period. Introduce formulas for finding these quantities and units of measurement.

Tasks:

Educational : to give students an idea of ​​the curvilinear movement of its trajectory, the quantities that characterize it, the units of measurement of these quantities and formulas for calculation.
Developmental : continue to develop the ability to apply theoretical knowledge to solve practical problems, develop interest in the subject and logical thinking.
Educational : continue to develop students' horizons; the ability to keep notes in notebooks, observe, notice patterns in phenomena, and justify their conclusions.

Lesson type: combined

Methods: visual, verbal, elements of critical thinking, demonstration experiment.

Equipment: inclined chute, ball, ball on a string, toy car, spinning top, model of a clock with hands, multimedia projector, presentation.

PROGRESS OF THE LESSON

    Psychological mood. Physical minute.

    Checking homework.

    Frontal survey pp. 24-25 Questions for self-control.

    Checking the solution house. problems Exercise 5(2,3)

3.Call.

– What types of movement do you know?

How do body movements differ from each other?
– What is the difference between rectilinear and curvilinear movements?
– In what frame of reference can we talk about these types of motion?
– Compare trajectory and path for straight and curved motion.

2. Explanation of new material in combination with a demonstration experiment and conversation.

Teacher. Demonstration: a ball falling vertically, rolling down a chute, a ball spinning on a string, a toy car moving on a table, a tennis ball thrown at an angle to the horizon falling.

Teacher. How do the motion trajectories of the proposed bodies differ? (Students' answers)
Try to give it yourself definitions curvilinear and rectilinear movements. (Record in notebooks):
– straight motion– movement along a straight path, and the direction of the force and velocity vectors coincide ;

– curvilinear movement– movement along an indirect trajectory.

Consider two examples of curvilinear movement: along a broken line and along a curve

Teacher: How do these trajectories differ?

Student. In the first case, the trajectory can be divided into straight sections and each section can be considered separately. In the second case, you can divide the curve into circular arcs and straight sections. Thus, this movement can be considered as a sequence of movements occurring along circular arcs of different radii

Teacher. Give examples of rectilinear and curvilinear motion that you have encountered in life.

Teacher. Circular motion is often characterized not by the speed of movement, but by the period of time during which the body makes one full revolution. This quantity is called circulation period and is denoted by the letter T. (Write down the definition of the period).

Student message. A period is a quantity that occurs quite often in nature and technology. Yes, we know. That the Earth rotates around its axis and the average rotation period is 24 hours. A complete revolution of the Earth around the Sun occurs in approximately 365.26 days. The impellers of hydraulic turbines make one full revolution in a time of 1 second. A helicopter rotor has a rotation period of 0.15 to 0.3 seconds. The period of blood circulation in humans is approximately 21-22 seconds.

Teacher. The movement of a body in a circle can be characterized by another quantity - the number of revolutions per unit time. They call her frequency circulation: ν = 1/T. Frequency unit: s –1 = Hz. ( Write definition, unit and formula)

Student message. The crankshafts of tractor engines have a rotation speed of 60 to 100 revolutions per second. The gas turbine rotor rotates at a frequency of 200 to 300 rps. A bullet fired from a Kalashnikov assault rifle rotates at a frequency of 3000 rps.
To measure frequency, there are instruments, so-called frequency measuring circles, based on optical illusions. On such a circle there are black stripes and frequencies. When such a circle rotates, the black stripes form a circle at a frequency corresponding to this circle. Tachometers are also used to measure frequency .

Work on creating a concept table using§7

Circulation period

T = 1/ ν

T = t/n

the period of time during which a body makes one complete revolution

Frequency

s –1 = Hz.

ν = 1/T

ν = n/t

number of revolutions per unit time

Cyclic frequency

rad/s

= 2 ν

= 2/T

4. Reinforcing the material Teacher. In this lesson we became acquainted with the description of curvilinear motion, with new concepts and quantities. Answer me the following questions:
– How can you describe curvilinear movement?
– What is called angular movement? In what units is it measured?
– What are period and frequency called? How are these quantities related to each other? In what units are they measured? How can they be identified?

6. Control and self-test

Teacher. Next test task, as you have learned new material. Testing.

1. An example of curvilinear movement is...

a) falling of a stone;
b) turn the car to the right;
c) sprinter running 100 meters.

2. The minute hand of a clock makes one full revolution. What is the period of circulation?

a) 60 s; b) 1/3600 s; c) 3600 s.

3. A bicycle wheel makes one revolution in 4 s. Determine the rotation speed.

a) 0.25 1/s; b) 4 1/s; c) 2 1/s.

Test 2

1. An example of curvilinear movement is...

a) movement of the elevator;
b) a ski jump from a springboard;
c) a cone falling from the lower branch of a spruce tree in calm weather.

2. The second hand of the watch makes one full revolution. What is its circulation frequency?

a) 1/60 s; b) 60 s; c) 1 s.

3. The car wheel makes 20 revolutions in 10 s. Determine the period of revolution of the wheel?

a) 5 s; b) 10 s; c) 0.5 s.

Answers to test 1: b; V; A; V; V
Answers to test 2: b; A; V; V; b

7. Homework: § 7, compose problems to determine the period and frequency of circulation.

8. Summing up. Assessment using self-control cards

No.

Types of tasks

grade

Solving house problems

Drawing up a conceptual table

testing

Final grade

9. Reflection

"Self-assessment sheet."

Learned something new Learned

I'm upset Got joy

Surprised Didn't understand anything

Municipal budgetary educational institution "Chubaevskaya secondary school" of the Urmara district of the Chechen Republic

PHYSICS LESSON in 9TH GRADE

“Rectilinear and curvilinear movement.

Movement of a body in a circle."

Teacher: Stepanova E.A.

Chubaevo – 2013


Subject: Rectilinear and curvilinear movement. Movement of a body in a circle with a constant absolute speed.

Objectives of the lesson: to give students an idea of ​​rectilinear and curvilinear motion, frequency, period. Introduce formulas for finding these quantities and units of measurement.
Educational objectives: to form the concept of rectilinear and curvilinear motion, the quantities that characterize it, the units of measurement of these quantities and formulas for calculation.
Developmental tasks: continue to develop the skills to apply theoretical knowledge to solve practical problems, develop interest in the subject and logical thinking.
Educational objectives: continue to develop students’ horizons; the ability to keep notes in notebooks, observe, notice patterns in phenomena, and justify their conclusions.

Equipment: Presentation. Computer. Multimedia projector Ball, ball on a string, inclined chute, ball, toy car, spinning top, clock model with hands, stopwatches

Lesson progress

I. Organizational moment. Introductory word from the teacher. Hello, my young friends! Let me start our lesson today with these lines: “Terrible mysteries of nature hang everywhere in the air” (N. Zabolotsky, poem “Mad Wolf”) (slide 1)

2. Updating knowledge

- What types of movement do you know?- What is the difference between rectilinear and curvilinear movements?- Compare trajectory and path for straight and curved movements. Teacher: We know that all bodies attract each other. In particular, the Moon, for example, is attracted to the Earth. But the question arises: if the Moon is attracted to the Earth, why does it revolve around it instead of falling towards the Earth? (sl-)

In order to answer this question, it is necessary to consider the types of motion of bodies. We already know that movement can be uniform and uneven, but there are other characteristics of movement (slide)

3. Problem situation: How are the following movements different?

Demonstrations: falling a ball in a straight line, rolling a ball along a straight chute. And along a circular path, the rotation of a ball on a string, the movement of a toy car on the table, the movement of a ball thrown at an angle to the horizon...( by type of trajectory)

Teacher: Based on the type of trajectory, these movements can be divide for movement in a straight line and along a curved line .(slide)

Let's try to give definitions curvilinear and rectilinear movements. ( Writing in a notebook) rectilinear movement - movement along a straight path. Curvilinear movement is movement along an indirect (curved) trajectory.

4. So, the topic of the lesson

Rectilinear and curvilinear movement. Circular movement(slide)

Teacher: Let's consider two examples of curvilinear movement: along a broken line and along a curve (draw). How are these trajectories different?

Students: In the first case, the trajectory can be divided into straight sections and each section can be considered separately. In the second case, you can divide the curve into circular arcs and straight sections. T.ob. this movement can be considered as a sequence of movements occurring along circular arcs of different radii. Therefore, to study curvilinear motion, you need to study movement in a circle.(slide 15)

Message 1 Movement of a body in a circle

In nature and technology very often there are movements whose trajectories are not straight, but curved lines. This is a curvilinear movement. Planets and artificial satellites of the Earth move along curvilinear trajectories in outer space, and on Earth all kinds of means of transport, parts of machines and mechanisms, river waters, atmospheric air, etc.

If you press the end of a steel rod against a rotating grindstone, the hot particles coming off the stone will be visible in the form of sparks. These particles fly at the speed they had at the moment they left the stone. It is clearly seen that the direction of movement of the sparks coincides with the tangent to the circle at the point where the rod touches the stone. On a tangent Splashes from the wheels of a skidding car are moving. (Sketch.)

Direction and velocity module

Teacher: Thus, the instantaneous speed of the body in different points curvilinear trajectory has different direction. In absolute terms, the speed can be the same everywhere or vary from point to point. (slide)

But even if the speed module does not change, it cannot be considered constant. Speed ​​- vector quantity. For a vector quantity, the magnitude and direction are equally important. And once speed changes, which means there is acceleration. Therefore, curvilinear movement is always accelerating movement, even if the absolute value of the speed is constant .(slide)(video1)

Acceleration body moving uniformly in a circle at any point centripetal, i.e. directed along the radius of the circle towards its center. At any point, the acceleration vector is perpendicular to the velocity vector. (Draw)

Modulus of centripetal acceleration: a c =V 2 /R ( write the formula), where V is the linear speed of the body, and R is the radius of the circle. (slide)

Centripetal force is a force acting on a body during curvilinear motion at any time, always directed along the radius of the circle towards the center (as is centripetal acceleration). And the force acting on a body is proportional to acceleration. F=ma, then

Characteristics of body movement in a circle

Circular motion is often characterized not by the speed of movement, but by the period of time during which the body makes one full revolution. This quantity is called circulation period and is designated by the letter T. ( Write period definition). When moving in a circle, a body will return to its original point in a certain period of time. Therefore, the circular motion is periodic.

A period is the time of one complete revolution.

If a body makes N revolutions in time t, then how to find the period? (formula)

Let's find the connection between the period of revolution T and the magnitude of velocity for uniform motion in a circle of radius R. Because V=S/t = 2πR/T. ( Write the formula in your notebook)

Message2 A period is a quantity that occurs quite often in nature and technology. Yes, we know. That the Earth rotates around its axis and the average rotation period is 24 hours. A complete revolution of the Earth around the Sun occurs in approximately 365.26 days. The impellers of hydraulic turbines make one full revolution in a time of 1 second. A helicopter rotor has a rotation period of 0.15 to 0.3 seconds. The period of blood circulation in humans is approximately 21-22 seconds.

Teacher: The movement of a body in a circle can be characterized by another quantity - the number of revolutions per unit time. They call her frequency circulation: ν= 1/T. Frequency unit: s -1 =Hz. ( Write definition, unit and formula)(slide)

How to find the frequency if a body makes N revolutions in time t (formula)

Teacher: What conclusion can be drawn about the relationship between these quantities? (period and frequency are mutual reciprocals)

Message3 The crankshafts of tractor engines have a rotation speed of 60 to 100 revolutions per second. The gas turbine rotor rotates at a frequency of 200 to 300 rps. Bullet. Flying out of a Kalashnikov assault rifle, it rotates at a frequency of 3000 rps. To measure frequency, there are instruments, so-called frequency measuring circles, based on optical illusions. On such a circle there are black stripes and frequencies. When such a circle rotates, the black stripes form a circle at a frequency corresponding to this circle. Tachometers are also used to measure frequency. (slide)

Connection Rotation speed and rotation period

ℓ - circumference

ℓ=2πr V=2πr/T

Additional characteristics of circular motion. (slide)

Teacher: Let us remember what quantities characterize rectilinear motion?

Movement, speed, acceleration.

Teacher: by analogy, movement in a circle - the same quantities - angular displacement, angular velocity and angular acceleration.

Angular displacement: (slide) This is the angle between two radii. Designated – Measured in rad or deg.

Teacher: Let's remember from the algebra course how the radian is related to the degree?

2pi rad = 360 deg. Pi = 3.14, then 1 rad = 360/6.28 = 57 degrees.

Angular velocity w=

Unit of measurement of angular velocity - rad/s

Teacher:. Think about what the angular velocity will be equal to if the body has completed one full revolution?

Student. Since the body has completed a full revolution, the time of its movement is equal to the period, and the angular displacement is 360° or 2. Therefore, the angular velocity is equal to.

Teacher: So what did we talk about today? (about curvilinear motion)

5. Questions for consolidation.

What kind of movement is called curvilinear?

Which motion is a special case of curvilinear motion?

What is the direction of instantaneous velocity during curvilinear motion?

Why is acceleration called centripetal?

What are period and frequency called? What units are they measured in?

How are these quantities interrelated?

How can we describe curvilinear motion?

What is the direction of acceleration of a body moving in a circle with a constant velocity?

6. Experimental work

Measure the period and frequency of a body suspended on a thread and rotating in a horizontal plane.

(on your desks you have bodies suspended by strings, a stopwatch. Rotate the body in a horizontal plane evenly and measure the time of 10 complete rotations. Calculate the period and frequency)

7. Consolidation. Problem solving. (slide)

    A.S. Pushkin. "Ruslan and Lyudmila"

At Lukomorye green oak,

Golden chain on the oak tree

Day and night the cat is a scientist

Everything goes around and around in a chain.

Q: What is this cat movement called? Determine the frequency and period and angular velocity if in 2 minutes. He does 12 laps. (answer: 0.1 1/s, T=10s, w=0.628rad/s)

    P.P. Ershov “The Little Humpbacked Horse”

Well, this is how our Ivan goes

Behind the ring on the okiyan

The little hunchback flies like the wind,

And the start for the first evening

I covered a hundred thousand versts

And I didn’t rest anywhere.

Q: How many times did the Little Humpbacked Horse circle the Earth during the first evening? The earth has the shape of a ball, and one mile is approximately 1066 m. (answer: 2.5 times)

8.Test Checking the assimilation of new material(tests on paper)

Test 1.

1. An example of curvilinear movement is...

a) falling of a stone;
b) turn the car to the right;
c) sprinter running 100 meters.

2. The minute hand of a clock makes one full revolution. What is the period of circulation?

a) 60 s; b) 1/3600 s; c) 3600 s.

3. A bicycle wheel makes one revolution in 4 s. Determine the rotation speed.

a) 0.25 1/s; b) 4 1/s; c) 2 1/s.

4. The propeller of a motor boat makes 25 revolutions in 1 s. What is the angular velocity of the propeller?

a) 25 rad/s; b) /25 rad/s; c) 50 rad/s.

5. Determine the rotation speed of the electric drill drill if its angular speed is 400 .

a) 800 1/s; b) 400 1/s; c) 200 1/s.

Answers: b; V; A; V; V.

Test 2.

1. An example of curvilinear movement is...

a) movement of the elevator;
b) a ski jump from a springboard;
c) a cone falling from the lower branch of a spruce tree in calm weather.

The second hand of a watch makes one full revolution. What is its circulation frequency?

a) 1/60 s; b) 60 s; c) 1 s.

3. The car wheel makes 20 revolutions in 10 s. Determine the period of revolution of the wheel?

a) 5 s; b) 10 s; c) 0.5 s.

4. The rotor of a powerful steam turbine makes 50 revolutions in 1 s. Calculate the angular velocity.

a) 50 rad/s; b)/50 rad/s; c) 10 rad/s.

5. Determine the rotation period of the bicycle sprocket if the angular velocity is equal.

a) 1 s; b) 2 s; c)0.5 s.

Answers: b; A; V; V; b.

Self-test

9. Reflection.

Let's fill it out together ZUH mechanism (I know, I found out, I want to know)

10.Summing up, grades for the lesson

11. Homework paragraphs 18,19,

home study: calculate, if possible, all the characteristics of any rotating body (bicycle wheel, minute hand of a clock)

    Ya. I. Perelman. Entertaining physics. Book 1 and 2 - M.: Nauka, 1979.

    S. A. Tikhomirova. Didactic material in physics. Physics in fiction. 7 – 11 grades. – M.: Enlightenment. 1996.

Lesson in 9th grade.

Subject: Rectilinear and curvilinear movement. Movement on

circles with a constant modulus speed.

Lesson objectives: 1. Give schoolchildren an idea of ​​the curvilinear

movement, period, frequency; idea of ​​direction and

value of speed and acceleration when moving along

circles.

2. Continue to develop the ability to apply

theoretical knowledge for solving practical problems;

promote the development of the ability to compare,

analyze.

3. Instill in students an interest in science and the subject of physics.

Equipment:For the teacher– slides “Curvilinear and rectilinear

movement", "Circular movement", tripod with ball

on a thread, a tripod with a fixed groove, a magnet,

crossword.

For students– a tripod with a ball attached to a thread,

clock with second hand, sheets with test tasks,

cards.

Board design: the topic of the lesson is written on the board, the crossword puzzle grid is drawn, tasks for independent solution are written, the student prepares a drawing for the answer, written down homework.

Lesson plan.

I. Organizational moment

II. Updating the acquired knowledge.

III. Explanation of new material.

IV. Fixing the material.

V. Knowledge control.

VI. Homework.

VII. Summing up the lesson.
Lesson progress

1.Organizational moment.

TEACHER: Hello! I am glad to welcome you to the physics lesson.

The great French physicist Pascal said: “... our knowledge can never have an end precisely because the subject of knowledge is infinite.”

Today in class we will try to make a little progress in our knowledge of the world around us.

Let's remember what we already studied in 9th grade.

STUDENT: We studied rectilinear uniform and rectilinear uniformly accelerated motion.

TEACHER: Is only rectilinear motion found in the world around us?

STUDENT: No. Straight-line movement is rare. More often, bodies move not in a straight line, but along a curved line.

TEACHER: So, what is the task before us, what should we do in class today?

STUDENT: We will study curvilinear motion.

TEACHER: What does it mean to “study movement”?

STUDENT: To study movement means to introduce some of its characteristics.

TEACHER: Right! That is, today in the lesson we will look at the features of curvilinear movement, introduce new characteristics of movement and, as an example of curvilinear movement, consider movement in a circle.

2. . Updating the acquired knowledge.

TEACHER: But before moving on to a new topic, let us remember what we know about motion, about basic physical quantities and concepts. Let's do a physical warm-up and solve a crossword puzzle (The crossword puzzle grid is drawn on a piece of Whatman paper. The student enters the correct answer into the crossword puzzle grid, students are asked additional questions. Type of work - whole class, individual).

1. Physical vector quantity,

measured in meters.

(move)

1a. What is movement?

1b. What are the units of movement?

You know?

2. Unit of measurement of angle.

2a. What device is used to measure angles?

3. A physical quantity, the units of measurement of which are century, year.

3a. Name the SI unit of time.

3b. What instruments are used to measure time?

4. A physical quantity showing the speed of speed measurement.

(acceleration)

4a. What is acceleration?

4b. In what units is acceleration measured?

5. Path length.

5a. Imagine that you ran one lap around the stadium. What is greater - the path or the movement?

5b. When is path equal to displacement?

6. Physical vector quantity characterizing the speed of movement.

(speed)

6a. What units of speed do you know?

6b. What device measures speed?

7. One of the main units of measurement in physics.

7a. name the SI base units.

7b. What physical quantities correspond to them?

8. Change in body position in space over time.

(movement)

8a. Name the types of motion depending on acceleration.

8b. What kind of motion is called uniform? Uniformly accelerated?

While the class is working on the crossword puzzle, 5 students (strong) complete the task on the spot using cards.

3. Explanation of new material.

TEACHER: We solved the crossword puzzle. The word that will be key in the study is highlighted vertically. new topic"Curvilinear movement." What is this word?

STUDENT: Trajectory.

TEACHER: Let's remember what a trajectory is?

STUDENT: A trajectory is a line along which a body moves.

TEACHER: Do movements differ according to the type of trajectory? Let's look at examples of movement.

Demonstration: 1) a plasticine ball falling vertically down; 2) rolling the ball along the chute; 3) rotation of the ball on the thread; 4) rolling the ball along the chute next to the magnet.

TEACHER: How can observed movements be classified?

STUDENT: the falling and rolling of the ball is a rectilinear movement, and the rotation and rolling next to the magnet is a curvilinear movement.

TEACHER: Remember the definition of rectilinear motion and, by analogy, try to give a definition of curvilinear motion. Write it down in your notebook (Write it down yourself, then read it out).

STUDENT: Curvilinear movement is movement whose trajectory is a curved line.

TEACHER: Give examples of linear and curved motion.

STUDENTS: (suggested answers) rectilinear: a pencil falling from a desk, a tram moving without turning; curvilinear: planetary movement, car turning

TEACHER: Now let’s introduce the characteristics of curvilinear motion, thinking about what quantities to describe it. Consider two trajectories of curvilinear motion. Think about how to describe the first type of movement?

STUDENT: In the first case, the trajectory can be divided into rectilinear sections, as we know how to describe rectilinear motion.

TEACHER: Right! And in the second case, what proposals will there be? How to describe the second type of movement?

STUDENT: The trajectory can be divided into circular arcs.

TEACHER: Do this in your notebook using compasses (students complete the construction independently). That is, curvilinear movement can be represented as movement in a circle. Consider the motion of a body in a circle. This is the simplest and most common type of curvilinear movement.

Demonstration of a slide of movement in a circle.

TEACHER: Give more examples of the motion of bodies in a circle.

STUDENT: Movement of planets, clock hands.

TEACHER: Well done! To characterize the movement, you need to introduce some quantities. Think about what is special about moving in a circle?

STUDENT: This movement is repeated.

TEACHER: Let's write down the characteristics of motion in a circle.

First characteristic:

Period T is the time of one full revolution.

TEACHER: What is it measured in?

STUDENT: Since this is time, it is measured in seconds.

TEACHER: If during time t the body makes N revolutions, how to find the period?

STUDENT: Need to total time divide by the number of revolutions.

TEACHER: Right! Let's write the formula:

T=

TEACHER: Now let’s hear a message about the period (the message was prepared by the student in advance).

Message 1. Period is a quantity that is found quite often in nature, science and technology. So, we know that the Earth rotates around its axis and the average period of this rotation is 24 hours; a complete revolution of the Earth around the Sun occurs in approximately 365.26 days; the impellers of hydraulic turbines make one full revolution in 1 s, and the propeller of a medium or light helicopter has a rotation period from 0.15 to 0.3 s; The period of blood circulation in humans is approximately 21-22 s.

TEACHER: Give more examples of rotation periods of bodies known to you (write 1-2 examples in your notebook yourself).

So, the period of rotation of the Earth and the Moon, what are they equal to?

STUDENT: Rotation period

The Earth is 365 s, and the Moon is 30 s.

TEACHER: Who spins faster?

STUDENT: The Moon rotates faster.

TEACHER: So what is the second characteristic of movement?

STUDENT: Speed ​​of rotation.

TEACHER: Right! Or frequency. Frequency () is the number of revolutions per unit of time.

Unit of measurement:  = s -1.

If during time t the body makes N revolutions, then the rotation frequency  = .

Look carefully at the formulas for period and frequency that we wrote down, what conclusion can be drawn about the relationship between the period and frequency values?

STUDENT: Period and frequency are mutually inverse quantities, period is inversely proportional to frequency, and frequency is inversely proportional to period.

TEACHER: Write down this dependence yourself in your notebook.

What is frequency and why is it interesting? Let's hear a message (prepared in advance by the student).

Message 2. To measure frequency, there are special instruments - the so-called circles for measuring frequency, the action of which is based on optical illusion. On each such circle there are black stripes and the frequency value is indicated. When rotating, the black stripes form a circle of a certain thickness at the corresponding frequency. Tachometers are also used to measure frequency. Here is some information about the speed of rotation of technical devices: crankshafts of tractor engines have a speed of rotation from 60 to 100 1/s, the rotor of a gas turbine rotates with a frequency of 200 to 300 1/s; a bullet fired from a Kalashnikov assault rifle rotates at a frequency of 3000 1/s.

TEACHER: How else do we characterize any movement?

STUDENT: Any movement is characterized by speed.

TEACHER: Let's think about the direction of speed when moving in a circle? Let's remember: a car is slipping, where does the dirt fly out from under the wheels? Introduced?

Now open the textbook page 69 figure 38 ( independent work with a textbook). What can be concluded from these examples?

STUDENT: The speed when moving in a circle is directed tangentially.

ACCOUNTANT: Write this down in your notebook and sketch the direction of speed when moving in a circle

Now look at the drawing. What can you say about the direction of speed? Does it change?

STUDENT: Yes, the direction of speed changes.

TEACHER: Can we say that the speed changes?

STUDENT: Yes. The speed changes.

TEACHER: Why do we say this? Remember what the speed is? Vector or scalar?

STUDENT: Speed ​​is a vector quantity, i.e. both value and direction are important for it. And if the direction changes, then the speed itself changes.

TEACHER: So, what kind of motion is it in a circle: uniform or uniformly accelerated?

STUDENT: This is an accelerated movement.

TEACHER: Write this conclusion in your notebook (by yourself).

So, what is the fourth characteristic of curvilinear motion?

STUDENT: This is acceleration.

TEACHER: Let's find out what the acceleration is equal to and where it is directed when moving in a circle.


Let us determine the direction of the acceleration of a body if it moves in a circle with a constant velocity in absolute value. To do this, let's look at the figure. It depicts a body (material point) moving in a circle of radius r. In a very short period of time t, this body moves from point A to point B, which is located very close to point A. In this case, the difference in the length of the arc AB and the chord
can be neglected and assume that the body moves along a chord. But the directions of the velocities v 0 and v that the body had at points A and B, respectively, are still different. The acceleration of a body is determined by the formula:

.

The acceleration vector is codirectional with a vector equal to the geometric speed difference (v – v 0). To find this vector, move the vector parallel to itself at point A and connect the ends of the velocity vectors with a straight line segment directed from To . This will be the vector (v – v 0). We see that it is directed inside the circle.

As the time interval t approaches zero, the segment AB contracts to a point. The acceleration vector is directed towards the center of the circle. Therefore, the acceleration with which a body moves in a circle with a constant absolute speed is called centripetal. Centripetal acceleration at any point is directed along the radius of the circle towards its center.

TEACHER: Write down in your notebook where the acceleration is directed when moving in a circle. Fine.

Considering the similarity of triangles, we get

The following students will prepare the derivation of this formula for the next lesson. . . (the task is given to students with high level knowledge).

4. Consolidation.

TEACHER: So, what did we learn about curvilinear motion today? Remember, look at your notes.

Now let’s check whether you have understood today’s topic well. You need to solve an experimental problem. We work in groups of 4 people (students have a tripod with a ball on a string on their tables).

TASK 1: Determine the period of revolution of the ball.

TASK 2 (for students with a high level of knowledge). Explore what determines the period of rotation?

Then we discuss the results and find out that the rotation period depends on the rotation speed and radius.

TEACHER: Now let’s digress a little and combine physics and lyrics.

(There are 2 problems on the screen. Solve them independently, then check each other).

1 – option.

Task 1. A.S. Pushkin "Ruslan and Lyudmila"

There is a green oak near the Lukomorye,

Golden chain on the oak tree;

Day and night the cat is a scientist

Everything goes around and around in a chain. . .

What is this cat movement called? Determine the frequency of his movement if in 1 minute he makes 6 “circles” (revolutions). What is the period?

ANSWERS:  = 0.1 s -1, T = 10 s.

2 – option.

Problem 2. A.M. Gorky "Makar Chudra"

And they both (Loiko Zobar and Rada. - A.S.) circled in the darkness of the night smoothly and silently, and the handsome Loiko could not catch up with the proud Rada.

Determine the hero's circulation period if his circulation frequency is 2 s -1.

ANSWER: T = 0.5 s.

(brief discussion of tasks).

TEACHER: It's time to check how you have learned the new material. So, there are tests on the table in front of you. Tests at different levels: initial, intermediate, sufficient levels. Write your name on pieces of paper and start working. The test takes 5 minutes to complete.

After completing the test, the correct answers are revealed. The guys evaluate themselves (self-control).

Evaluation criteria:

Sufficient level: “5” - 5

Average level: “4” - 4-5

Entry level: “3” - 4-5

(Students hand in sheets with grades).

5. Homework.

Write in the diary: § 18, 19 (answer according to a generalized plan)

“5” - Ex. 17(3) orally, Ex. 18(4) in writing.

“4” - Ex. 17(2) orally, Ex. 18(1) in writing.

6. Summing up the lesson.

TEACHER: So, what did we study today, what did we learn new?

The concept of curvilinear motion was introduced.

Its characteristics were introduced: period, frequency, speed, acceleration.

Let's remember what period and frequency are; where is the speed directed when moving in a circle; where is the acceleration directed and what is it equal to?

TEACHER: Well done! Well, who can be rewarded with an assessment?

Students evaluate the work of their classmates (peer assessment).

Evaluated:

    Working with a crossword puzzle (individual students).

    Students' answers from their seats during the explanation.

    Answers from students who prepared the message.

    Answer from a student explaining a new topic.

In addition, all students received marks for completing the test and 5 students will receive marks for working on the cards.

TEACHER: Thanks for the lesson. Goodbye.

TASKS ON THE CARDS

    Describe the motion of a body whose velocity projection graph is shown in the figure.

    The equation of body motion is s = 2t + t 2. Describe this movement (indicate the values ​​of the quantities characterizing it), construct a graph of s x (t).

    The time dependence of the coordinates of a point moving along the x axis has the form: x = 2 - 10t + 3t 2. Describe the nature of the movement. What are the initial velocity and acceleration? Write down the equation for the velocity projection.

    A freight train leaving the station was traveling at a speed of 36 km/h. After 0.5 hours, a fast train departed in the same direction, the speed of which was 72 km/h. How long after the freight train leaves will the fast train catch up with it?

    A skier covered a slope 100 m long in 20 s, moving with an acceleration of 0.3 m/s 2 . What is the speed of the skier at the beginning and end of the slope?

Answers to tests

Entry level

B-1. B-2.

Intermediate level

B-1. B-2.

Sufficient level

We know that all bodies attract each other. In particular, the Moon, for example, is attracted to the Earth. But the question arises: if the Moon is attracted to the Earth, why does it revolve around it instead of falling towards the Earth?

In order to answer this question, it is necessary to consider the types of motion of bodies. We already know that movement can be uniform and uneven, but there are other characteristics of movement. In particular, depending on the direction, rectilinear and curvilinear movement are distinguished.

Straight-line movement

It is known that a body moves under the influence of a force applied to it. You can do a simple experiment showing how the direction of movement of a body will depend on the direction of the force applied to it. To do this, you will need an arbitrary small object, a rubber cord and a horizontal or vertical support.

Ties the cord at one end to the support. At the other end of the cord we attach our object. Now, if we pull our object a certain distance and then release it, we will see how it begins to move in the direction of the support. Its movement is caused by the elastic force of the cord. This is how the Earth attracts all bodies on its surface, as well as meteorites flying from space.

Only instead of the elastic force, the force of attraction acts. Now let’s take our object with an elastic band and push it not in the direction towards/away from the support, but along it. If the object were not secured, it would simply fly away. But since it is held by a cord, the ball, moving to the side, slightly stretches the cord, which pulls it back, and the ball slightly changes its direction towards the support.

Curvilinear movement in a circle

This happens at every moment of time; as a result, the ball does not move along the original trajectory, but also not straight to the support. The ball will move around the support in a circle. The trajectory of its movement will be curvilinear. This is how the Moon moves around the Earth without falling on it.

This is how the Earth's gravity captures meteorites that fly close to the Earth, but not directly at it. These meteorites become satellites of the Earth. Moreover, how long they will stay in orbit depends on what their initial angle of motion was relative to the Earth. If their movement was perpendicular to the Earth, then they can remain in orbit indefinitely. If the angle was less than 90˚, then they will move in a descending spiral, and will gradually fall to the ground.

Circular motion with a constant modulus speed

Another point to note is that the speed of curvilinear motion around a circle varies in direction, but is the same in value. And this means that movement in a circle with a constant absolute speed occurs uniformly accelerated.

Since the direction of movement changes, it means that the movement occurs with acceleration. And since it changes equally at each moment of time, therefore, the movement will be uniformly accelerated. And the force of gravity is the force that causes constant acceleration.

The Moon moves around the Earth precisely because of this, but if suddenly the Moon’s movement ever changes, for example, a very large meteorite crashes into it, then it may well leave its orbit and fall to the Earth. We can only hope that this moment never comes. Such things.