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Movement in a circle Physics teacher Alexander Mikhailovich Fedorov Municipal Educational Institution Kyukyai Secondary School Suntarsky ulus Republic of Sakha

In the life around us, we encounter movement in a circle quite often. This is how the hands of watches and the gears of their mechanisms move; this is how cars move on convex bridges and on curved sections of roads; Artificial Earth satellites move in circular orbits.

The instantaneous speed of a body moving in a circle is directed tangentially to it at this point. It's not difficult to observe.

We will study the motion of a point along a circle with a constant absolute speed. It is called uniform circular motion. The speed of a point moving in a circle is often called linear speed. If a point moves uniformly around a circle and in time t covers a path L equal to the length of the arc AB, then the linear velocity (its modulus) is equal to V = L/t A B

Uniform motion in a circle is motion with acceleration, although the velocity module does not change. But the direction is constantly changing. Therefore, in this case, acceleration a should characterize the change in speed in direction. O v a The acceleration vector a, when a point moves uniformly around a circle, is directed radially to the center of the circle, therefore it is called centripetal. The acceleration module is determined by the formula: a = v 2 /R, Where v is the module of the speed of the point, R is the radius of the circle.

PERIOD OF REVOLUTION The movement of a body in a circle is often characterized not by the speed of movement v, but by the period of time during which the body makes one full revolution. This quantity is called the orbital period. It is designated by the letter T. When calculating, T is expressed in seconds. During a time t equal to period T, the body travels a path equal to the circumference: L = 2 R. Therefore, v = L/T=2 R/T. Substituting this expression into the formula for acceleration, we get another expression for it: a= v 2 /R = 4 2 R/T 2.

Frequency of rotation The movement of a body in a circle can be characterized by another quantity - the number of revolutions in a circle per unit time. It is called the frequency of circulation and is denoted by the Greek letter  (nu). Frequency and period are related by the following relationship: = 1/T The unit of frequency is 1/s or Hz. Using the concept of frequency, we obtain formulas for speed and acceleration: v = 2R/T = 2R; a = 4 2 R/T 2 = 4 2  2 R.

So, we have studied motion in a circle: Uniform motion in a circle is motion with acceleration a = v 2 /R. The period of revolution is the period of time during which a body makes one complete revolution. It is designated by the letter T. Circulation frequency is the number of revolutions in a circle per unit time. It is denoted by the Greek letter  (nu). The rotation frequency and period are related by the following relationship:  = 1/T Formulas for speed and acceleration: v = 2R/T = 2R; a = 4 2 R/T 2 = 4 2  2 R.

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On the topic: methodological developments, presentations and notes

A lesson in solving problems on the topic "Dynamics of motion in a circle." In the process of solving problems in groups, students learn from each other....

A lesson in learning a new topic using presentations, videos....

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1 2 Uniform motion in a circle is a motion in which a material point passes circles of equal length in equal intervals of time. Uniform motion in a circle Solution of problems 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk

Period of revolution 2 1 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH No. 3", Nizhnekamsk The time of one revolution around the circle is called the period of rotation T N - the number of revolutions made during time t. The unit of circulation frequency is 1 revolution per second (1 s -1)

3 2 10 1 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk Angular velocity

4 2 10 3 1 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH No. 3", Nizhnekamsk The modulus of the linear velocity vector is equal to:

5 2 10 3 4 1 6 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH No. 3", Nizhnekamsk The module of the centripetal acceleration vector is equal to:

6 2 10 3 4 5 1 7 8 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk Problem. What is the linear speed of the points on the wheel rim of a steam turbine with a wheel diameter of 1 m and a rotation speed of 300 rpm? Show solution

7 2 10 3 4 5 6 1 8 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk Problem. How many times will the centripetal acceleration of a body change if it moves uniformly around a circle of twice the radius with the same angular velocity? Show solution

8 2 10 3 4 5 6 7 1 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk Problem. The angular speed of the fan blades is 20π rad/s. Find the number of revolutions in 30 minutes. Show solution

1 Option 2 Option 1. The angular speed of the fan blades is 20π rad/s. Find the number of revolutions in 30 minutes. 2. The rotation speed of the aircraft propeller is 1500 rpm. How many revolutions will the propeller make on a path of 90 km at a flight speed of 180 km/h 2? A diesel locomotive moves at a speed of 60 km/h. How many revolutions per second do its wheels make if their radius is 50 cm? 1 . When turning, a tram car moves at a constant absolute speed of 5 m/s. What is its centripetal acceleration equal to if the radius of curvature of the path is 50 m. 9 2 10 3 4 5 6 7 8 1 Lyakhovich E.Yu., MBVSOU "VSOSH No. 3", Nizhnekamsk

ANSWERS 1 Option 2 Option 1. 18000. 2. 45000 2. 5.31 1 . 0.5 m/s 2. 1 2 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk

1 2 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU “VSOSH No. 3”, Nizhnekamsk Show solution

On the topic: methodological developments, presentations and notes

A lesson in solving problems on the topic "Dynamics of motion in a circle." In the process of solving problems in groups, students learn from each other....

A lesson in learning a new topic using presentations, videos....

The work is intended for 10th grade students, presented in two versions. Definition knowledge tasks, graphic tasks and matching tasks....

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In mechanics, examples teach as much as rules. I. Newton

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Terrible mysteries of nature hang in the air everywhere.N. Zabolotsky (from the poem “Mad Wolf”)

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A4. The body moves in a circle clockwise. Which of the vectors shown coincides in direction with the velocity vector of the body at point A? eleven; 2) 2; 3) 3; 4) 4.

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Movement of a body in a circle with a constant absolute speed. Lesson topic:

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Objectives: To repeat the features of curvilinear motion, to consider the features of circular motion, to get acquainted with the concept of centripetal acceleration and centripetal force, period and frequency of rotation, to find out the relationship between quantities.

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Conclusion page 70

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With uniform motion in a circle, the magnitude of its speed does not change. But speed is a vector quantity, and it is characterized not only by its numerical value, but also by its direction. With uniform motion in a circle, the direction of the velocity vector changes all the time. Therefore, such uniform motion is accelerated.

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When a body moves uniformly in a circle, the acceleration vector is always perpendicular to the velocity vector, which is directed tangentially to the circle.

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Conclusion page 72