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Circular Motion - By Matthew Hunter

A presentation on Circular Motion.

Matthew Hunter

on 20 September 2010

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Transcript of Circular Motion - By Matthew Hunter

Circular Motion By Matthew Hunter 2.1 - Uniform circular motion Equations you need to know! Frequency of rotation f = 1 _ T (T is the time for one rotation) The speed v of a point on the perimeter = circumference/time for 1 rotation = __ 2nr T = 2nrf A worked example! Have a try at this :) A cyclist is travelling at a speed of 25ms-1 on a bicycle which has wheels of radius 750mm. Calculate: a - The time for one rotation of the wheel. bi - The frequency of rotation of the wheel. ii - The number of rotations of the wheel in one minute 2.2 - Centripetal Acceleration A bit of information... The velocity of an object moving round a circle at constant speed continually changes direction. Because its velocity changes, the object therefore accelerates. The velocity of an object in uniform circular motion at any point is along the tangent of the circle at that point. The direction of hte velocity changes continuously as the object moves round on its circular path. The change in the direction of the velocity is towards the centre of the circle. So its acceleration is towards the centre of the circle and is referred to as centripetal acceleration. Centripetal acceleration a = v 2 _ r Solution! a. Rearranging speed v = 2nr __ T gives the time for 1 rotation, T = 2nr __ v Therefore, T = 2n x 0.75 ____ 25 = 0.19s bi. Frequency f = 1 _ T = 1 _ 0.19 = 5.3 Hz ii. Number of rotations in 1 minute = 60 x 5.3 = 318 Centripetal Force To make an object move round a circular path, it must be acted on by a resultant force which changes its direction of motion. The resultant force on an object moving round a cricle at constant speed is referred to as the centripetal force because it acts in the same direction as the centripetal acceleration, which is towards the centre of the circle. Centripetal force Centripetal force F = mv 2 ___ r = mw r 2 (when the equation for centripetal acceleration is included.) The London Eye! The London eye is a popular tourist attraction. The wheel has a diameter of 130m and takes passengers high above london. Each full rotation of the wheel takes 30 minutes. Each capsule therefore takes its passengers through an angle of 0.2 each second. Therefore, each capsule turns through an angle of 2 in 10s. 0 0 This doesn't seem very relevant so I'm going to stop writing it. f = 1 _ T
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