Lesson_Text_2.4 - 1 Lesson 2.4 Circular Motion 1. Motion in...

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1 Lesson 2.4 Circular Motion 1. Motion in a Circle θ r O A B Fig. 1 In this lesson we will discuss the case of an object moving around a circle of radius r with a uniform speed v. In the figure above, A is the initial position of an object and B is its position after t s. As the object goes round the circle, the line joining the position of the object to the center of the circle describes an angle θ . When the object completes one round, the angle described θ = 2 π . The rate at which θ changes is called the angular speed ( ϖ ) of the object. t θ ϖ = …(i) Angular speed ϖ is measured in rad.s -1 . The time taken by the object to go round the circle once is called the period (T) of the circular motion. The number of times the object goes round the circle is called the frequency (f) of the circular motion. 1 f T = …(ii) Frequency is measured in s -1 which is called a Hertz (Hz) When t = T, equation (i) above can be written as: 2 2 f T π = = ….(iii) If v is the linear speed of the object along the circle, then a distance of 2 π r is covered in a time T, the period. Thus we have: 2 r v r T = = …(iv)
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2 2. Centripetal Acceleration and Centripetal Force. According to the first law of motion, a force is required to change the direction of motion of an object. An object in circular motion continuously changes its direction of motion, and therefore, there must be continuous force acting on it to change its direction of motion. The function of this force is not to change the speed of the object, but to change its direction of motion. When the object goes round a circle, this force is always directed towards the center of the circle. The moment this force ceases, the object will move in a path tangential to the circle. This force that is directed towards the center of the circle to keep the object moving in a circle is called the centripetal force . The velocity of the object in circular motion is always tangential to the circle, which means it is continuously changing. In a uniform circular motion, the speed remains a constant, but the velocity continuously changes due to changes in the direction of motion. There is a change in velocity means that there is an acceleration, and this acceleration is caused by the centripetal force and is called the centripetal acceleration . Fig 2 below illustrates this. velocity v 1 velocity v 2 velocity v 3 centripetal force Fig. 2 velocity is tangential to the circle As the centripetal force is directed towards the center, the centripetal acceleration is also directed towards the center of the circle.
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3 Fig 3 below shows the positions and velocities of an object in uniform circular motion at two points A and B. The object in circular motion has a uniform speed v m/s. This means that the magnitudes of the velocity at point A and point B are both the same, namely v m/s. But the velocity at point B is v 1 and the velocity at point B is v 2 . v 1 and v 2 are different because of their different directions. v
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Lesson_Text_2.4 - 1 Lesson 2.4 Circular Motion 1. Motion in...

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