Post on the topic of rectilinear and curvilinear movement. Straight and curved movement. The movement of a body in a circle with a constant modulo velocity

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Think and answer! 1. What movement is called uniform? 2. What is called the speed of uniform movement? 3. What motion is called uniformly accelerated? 4. What is body acceleration? 5. What is relocation? What is a trajectory?

Lesson topic: Straight and curved motion. The movement of the body in a circle.

Mechanical movements Rectilinear Curvilinear elliptical movement Parabolic movement Hyperbolic movement Circular movement

Lesson objectives: 1. To know the main characteristics of curvilinear movement and the relationship between them. 2. Be able to apply the knowledge gained in solving experimental problems.

Study plan of the topic Study of new material Condition of rectilinear and curvilinear motion Direction of body velocity during curvilinear motion Centripetal acceleration Orbital period Orbital frequency Centripetal force Fulfillment of frontal experimental tasks Independent work in the form of tests Summing up

By the type of trajectory, the movement can be: Curvilinear Rectilinear

Conditions for rectilinear and curvilinear motion of bodies (Experiment with a ball)

page 67 Remember! Working with the tutorial

Circular motion is a special case of curvilinear motion

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Movement characteristics - linear speed of curvilinear movement () - centripetal acceleration () - period of revolution () - frequency of revolution ()

Remember. The direction of movement of particles coincides with the tangent to the circle

In curvilinear motion, the speed of the body is directed tangentially to the circle Remember.

In curvilinear motion, the acceleration is directed towards the center of the circle.

Why is the acceleration directed towards the center of the circle?

Determination of speed - speed - period of revolution r - radius of a circle

When a body moves in a circle, the modulus of the velocity vector may change or remain constant, but the direction of the velocity vector necessarily changes. Therefore, the velocity vector is a variable value. This means that movement in a circle always occurs with acceleration. Remember!

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Topic: Rectilinear and curvilinear motion. The movement of the body in a circle.

Objectives: To study the features of curvilinear movement and, in particular, movement along a circle.

Introduce the concept of centripetal acceleration and centripetal force.

Continue to work on shaping key competencies students: the ability to compare, analyze, draw conclusions from observations, generalize experimental data based on existing knowledge about body movement, form the ability to use basic concepts, formulas and physical laws of body movement when moving on a circle.

Foster independence, teach children to cooperate, foster respect for the opinions of others, awaken curiosity and observation.

Lesson equipment:computer, multimedia projector, screen, ball on an elastic band, ball on a thread, ruler, metronome, whirligig.

Registration: "We are truly free when we have retained the ability to reason for ourselves." Ceceron.

Lesson type: a lesson in learning new material.

During the classes:

Organizing time:

Problem statement: What types of movements have we studied?

(Answer: Rectilinear uniform, rectilinear uniformly accelerated.)

Lesson plan:

Updating basic knowledge (physical warm-up) (5 min)

What movement is called uniform?
What is called the speed of uniform movement?
What motion is called uniformly accelerated?
What is body acceleration?
What is relocation? What is a trajectory?

Main part. Learning new material. (11 minutes)

Formulation of the problem:

Assignment to students:Consider the spinning of a whirligig, the spinning of a ball on a thread (demonstration of experience). How can you characterize their movements? What is common in their movement?

Teacher: This means that our task in today's lesson is to introduce the concept of rectilinear and curvilinear motion. Body movements in a circle.

(recording the topic of the lesson in notebooks).

Lesson topic.

Slide number 2.

Teacher: To set goals, I propose to analyze the scheme of mechanical movement.(types of movement, scientific nature)

Slide number 3.

What goals will we set for our topic?

Slide number 4.

I suggest you study this topic as follows plan. (Highlight main)

Do you agree?

Slide number 5.

Take a look at the picture. Consider examples of the types of trajectories found in nature and technology.

Slide number 6.

The action of a force on a body in some cases can only lead to a change in the modulus of the velocity vector of this body, and in others - to a change in the direction of the velocity. Let us show this experimentally.

(Conducting experiments with a ball on an elastic band)

Slide number 7

Make a conclusion what the type of trajectory of movement depends on.

(Answer)

Now let's compare this definition with the one given in your textbook on page 67

Slide number 8.

Consider the drawing. How can curvilinear motion be associated with circular motion?

(Answer)

That is, the curved line can be rearranged as a set of arcs of circles of different diameters.

Let's conclude: ...

(Write in a notebook)

Slide number 9.

Consider what physical quantities characterize movement in a circle.

Slide number 10.

Consider an example of a car moving. What is flying out from under the wheels? How does it move? How are the particles directed? How are they protected from the action of these particles?

(Answer)

Let's make a conclusion :… (About the nature of particle motion)

Slide number 11

Let's look at how the speed is directed when the body moves in a circle. (Animation with a horse.)

Let's conclude: ... ( how the speed is directed.)

Slide number 12.

Let us find out how the acceleration is directed during curvilinear motion, which appears here due to the fact that there is a change in speed in the direction.

(Animation with a motorcyclist.)

Let's conclude: ... ( how is the acceleration directed)

Let's write down formula in a notebook.

Slide number 13.

Consider the drawing. Now we will find out why the acceleration is directed towards the center of the circle.

(teacher's explanation)

Slide number 14.

What conclusions can be drawn about the direction of speed and acceleration?

There are other characteristics of curvilinear motion. These include the period and frequency of rotation of the body in a circle. The speed and period are related by a ratio, which we will establish mathematically:

(The teacher writes on the chalkboard, students write in notebooks)

It is known, but the way, then.

Since then

Slide number 15.

What is general conclusion mono to do about the nature of the movement in a circle?

(Answer)

Slide number 16.,

According to Newton's II law, acceleration is always co-directed with the force, as a result of which it arises. This is also true for centripetal acceleration.

Let's make a conclusion : How is the force directed at each point of the trajectory?

(answer)

This force is called centripetal.

Let's write down formula in a notebook.

(The teacher writes on the chalkboard, students write in notebooks)

The centripetal force is created by all forces of nature.

Give examples of the action of centripetal forces by their nature:

elastic force (stone on a rope);
the force of gravity (planets around the sun);
frictional force (cornering).

Slide number 17.

For consolidation, I propose to conduct an experiment. To do this, we will create three groups.

Group I will establish the dependence of the speed on the radius of the circle.

Group II will measure the acceleration when moving in a circle.

Group III will establish the dependence of the centripetal acceleration on the number of revolutions per unit of time.

Slide number 18.

Summarizing... How does the speed and acceleration depend on the radius of the circle?

We will conduct testing for the initial consolidation. (7 minutes)

Slide number 19.

Assess your work in the lesson. Continue the sentences on the flyers.

(Reflection. Students voice individual answers aloud.)

Slide number 20.

Homework: §18-19,

Control. 18 (1, 2)

Additionally ex. 18 (5)

(Teacher comments)

Slide number 21.

Questions.

1. Consider Figure 33 a) and answer the questions: under what force does the ball acquire speed and move from point B to point A? As a result of what this power arose? How are the acceleration, the speed of the ball and the force acting on it directed? What is the trajectory of the ball?

The ball acquires speed and moves from point B to point A under the action of the elastic force F el, arising from the stretching of the cord. Acceleration a, the speed of the ball v, and the elastic force F eln acting on it, are directed from point B to point A, and therefore the ball moves in a straight line.

2. Consider Figure 33 b) and answer the questions: why did the elastic force appear in the cord and how is it directed in relation to the cord itself? What can be said about the direction of the ball's velocity and the elastic force of the cord acting on it? How does the ball move: straight or curved?

The elastic force F control in the cord arises due to its stretching, it is directed along the cord towards the point O. The velocity vector v and the elastic force F control lie on intersecting straight lines, the velocity is directed tangentially to the trajectory, and the elastic force is directed to the point O, therefore, the ball moves curvilinearly.

3. Under what condition does the body move rectilinearly under the action of force, and under what condition - curvilinearly?

A body under the action of a force moves rectilinearly if its velocity v and the force F acting on it are directed along one straight line, and, curvilinearly, if they are directed along intersecting straight lines.

Exercises.

1. The ball rolled along the horizontal surface of the table from point A to point B (fig. 35). At point B, a force F acted on the ball. As a result, it began to move to point C. In which of the directions indicated by arrows 1, 2, 3 and 4 could force F act?

Force F acted in direction 3, because the ball has a velocity component perpendicular to the initial direction of velocity.

2. Figure 36 shows the trajectory of the ball. On it, circles mark the position of the ball every second after the start of movement. Was the force acting on the ball in the range 0-3, 4-6, 7-9, 10-12, 13-15, 16-19? If the force was acting, how was it directed in relation to the velocity vector? Why did the ball turn to the left in section 7-9, and to the right in section 10-12 in relation to the direction of movement before the turn? Do not consider resistance to movement.

In sections 0-3, 7-9, 10-12, 16-19, an external force acted on the ball, changing the direction of its movement. In sections 7-9 and 10-12, a force acted on the ball, which, on the one hand, changed its direction, and on the other, slowed down its movement in the direction along which it was moving.

3. In Figure 37, the line ABCDE shows the trajectory of a certain body. In what areas did the force most likely act on the body? Could the body be acted upon by any force during its movement in other parts of this trajectory? Justify all answers.

The force acted in sections AB and CD, since the ball changed direction, however, in other sections, a force could also act, but not changing the direction, but changing the speed of its movement, which would not be reflected in its trajectory.

Movement is a change in position
bodies in space relative to others
bodies over time. Movement and
the direction of movement is characterized in
including speed. The change
speed and the type of movement itself are associated with
the action of force. If the body is affected
force, then the body changes its speed.

If the force is parallel
body movement, in one direction, then such
the movement will be straightforward.

Such a movement will be curvilinear,
when the speed of the body and the force applied to
this body, directed to each other relative
friend from a certain angle. In this case
speed will change its
direction.

So, with straightforward
motion, the velocity vector is directed to that
the same side as the force applied to
body. And curvilinear
movement is such movement,
when the vector of speed and force,
attached to the body, located under
some angle to each other.

Centripetal acceleration

CENTRAL
ACCELERATION
Consider a special case
curvilinear motion when the body
moves in a circle with a constant
speed module. When the body moves
in a circle at a constant speed, then
only the direction of speed changes. By
it remains constant to the module, and
the direction of the speed changes. Such
a change in speed leads to the presence of
acceleration body, which
called centripetal.

If the trajectory of the body is
curve, then it can be represented as
set of movements along arcs
circles, as shown in Fig.
3.

In fig. 4 shows how the direction changes
velocity vector. Speed with this movement
directed tangentially to a circle, along an arc
which the body moves. Thus, her
the direction is constantly changing. Even
the modulus remains constant,
a change in speed leads to the appearance of acceleration:

In this case, the acceleration will be
directed towards the center of the circle. therefore
it is called centripetal.
You can calculate it by the following
formula:

Angular velocity. relationship of angular and linear velocities

ANGULAR VELOCITY. COMMUNICATION
CORNER AND LINEAR
SPEEDS
Some characteristics of movement along
circles
Angular velocity is denoted in Greek
the letter omega (w), it says which
the angle rotates the body per unit of time.
This is the magnitude of the arc in degree measure,
traversed by the body for some time.
Note if solid rotates then
angular velocity for any points on this body
will be a constant value. Closer point
located towards the center of rotation or further -
it doesn't matter, i.e. does not depend on the radius.

The unit of measurement in this case will be
either degrees per second or radians in
give me a sec. Often the word "radian" is not written, but
just write s-1. For example, we will find,
what is the angular velocity of the Earth. Land
makes a full 360 ° turn in 24 hours, and in
in this case, we can say that
the angular velocity is.

Also note the relationship of the angular
speed and line speed:
V = w. R.
It should be noted that movement along
a circle with a constant speed is the quotient
case of motion. However, the movement in a circle
may be uneven. Speed can
change not only in direction and remain
the same in modulus, but also change in its own way
value, i.e., in addition to changing direction,
there is also a change in the speed module. IN
in this case we are talking about the so-called
accelerated movement in a circle.

With the help of this lesson, you will be able to independently study the topic “Rectilinear and curvilinear motion. The movement of a body in a circle with a constant modulus of speed ”. First, we characterize rectilinear and curvilinear motion, considering how the velocity vector and the force applied to the body are related in these types of motion. Next, we will consider a special case when a body moves in a circle with a constant modulus of speed.

In the previous lesson, we looked at issues related to the law universal gravitation... The topic of today's lesson is closely related to this law, we will turn to the uniform movement of the body around the circumference.

We said earlier that traffic - it is a change in the position of a body in space relative to other bodies over time. Movement and direction of movement are also characterized by speed. The change in speed and the type of movement itself are associated with the action of force. If a force acts on the body, then the body changes its speed.

If the force is directed parallel to the movement of the body, then such a movement will be straightforward(fig. 1).

Fig. 1. Straight-line movement

Curvilinear there will be such a movement when the speed of the body and the force applied to this body are directed relative to each other at a certain angle (Fig. 2). In this case, the speed will change its direction.

Fig. 2. Curvilinear motion

So, at straight motion the velocity vector is directed in the same direction as the force applied to the body. BUT curvilinear motion is a movement when the velocity vector and the force applied to the body are located at an angle to each other.

Consider a special case of curvilinear motion, when the body moves in a circle with a constant modulus of speed. When a body moves in a circle at a constant speed, then only the direction of the speed changes. In absolute value, it remains constant, but the direction of the velocity changes. Such a change in speed leads to the presence of an acceleration in the body, which is called centripetal.

Fig. 6. Movement along a curved path

If the trajectory of the body is a curve, then it can be represented as a set of movements along arcs of circles, as shown in Fig. 6.

In fig. 7 shows how the direction of the velocity vector changes. The speed during this movement is directed tangentially to the circle along the arc of which the body moves. Thus, its direction is constantly changing. Even if the speed remains constant in absolute value, a change in speed leads to the appearance of acceleration:

In this case acceleration will point towards the center of the circle. Therefore it is called centripetal.

Why is centripetal acceleration directed towards the center?

Recall that if the body moves along a curved trajectory, then its speed is tangential. The speed is vector quantity... A vector has a numerical value and a direction. Speed as the body moves continuously changes its direction. That is, the difference in speeds at different points in time will not be zero (), in contrast to the rectilinear uniform motion.

So, we have a change in speed over a period of time. The relation to is acceleration. We come to the conclusion that, even if the speed does not change in absolute value, the body performing uniform movement around the circumference, there is acceleration.

Where is this acceleration directed? Consider fig. 3. Some body moves curvilinearly (in an arc). The speed of the body at points 1 and 2 is tangential. The body moves uniformly, that is, the modules of the velocities are equal:, but the directions of the velocities do not coincide.

Fig. 3. The movement of the body in a circle

Let's subtract the velocity from it and get the vector. To do this, you need to connect the beginnings of both vectors. Move the vector to the beginning of the vector in parallel. We finish building to the triangle. The third side of the triangle will be the vector of the speed difference (Fig. 4).

Fig. 4. Velocity difference vector

The vector is directed towards the circle.

Consider a triangle formed by the velocity vectors and the difference vector (Fig. 5).

Fig. 5. The triangle formed by the velocity vectors

This triangle is isosceles (velocity modules are equal). This means that the angles at the base are equal. Let's write the equality for the sum of the angles of the triangle:

Let us find out where the acceleration is directed at a given point of the trajectory. To do this, we begin to bring point 2 closer to point 1. With such unlimited diligence, the angle will tend to 0, and the angle - to. The angle between the vector of the change in speed and the vector of the speed itself is. The velocity is directed tangentially, and the velocity vector is directed to the center of the circle. This means that the acceleration is also directed towards the center of the circle. That is why this acceleration is called centripetal.

How to find centripetal acceleration?

Consider the trajectory along which the body moves. In this case, it is a circular arc (Fig. 8).

Fig. 8. The movement of the body in a circle

The figure shows two triangles: a triangle formed by velocities and a triangle formed by radii and a displacement vector. If points 1 and 2 are very close, then the displacement vector will be the same as the path vector. Both triangles are isosceles with equal angles at the top. Thus, triangles are similar. This means that the corresponding sides of the triangles are related in the same way:

Moving is equal to the product of speed and time:. Substituting this formula, you can get the following expression for centripetal acceleration:

Angular velocity denoted by the Greek letter omega (ω), it tells about the angle at which the body rotates per unit of time (Fig. 9). This is the magnitude of the arc, in degree, traversed by the body in some time.

Fig. 9. Angular velocity

Note that if a rigid body rotates, then the angular velocity for any points on this body will be constant. Closer point is located to the center of rotation or further - it does not matter, that is, it does not depend on the radius.

The unit of measurement in this case will be either degrees per second () or radians per second (). Often the word "radian" is not written, but simply written. For example, let's find what the angular velocity of the Earth is equal to. The earth makes a full turn for an hour, and in this case we can say that the angular velocity is equal to:

Also pay attention to the relationship of angular and linear velocities:

Linear speed is directly proportional to radius. The larger the radius, the greater the linear velocity. Thus, moving away from the center of rotation, we increase our linear speed.

It should be noted that movement in a circle at a constant speed is a special case of movement. However, the movement around the circle can be uneven. The speed can change not only in the direction and remain the same in magnitude, but also change in its value, that is, in addition to changing the direction, there is also a change in the speed modulus. In this case, we are talking about the so-called accelerated motion in a circle.

What is a radian?

There are two units for measuring angles: degrees and radians. In physics, as a rule, the radian measure of the angle is the main one.

Construct a central angle that rests on an arc of length.

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