Motion in Two Dimensions – Uniform Circular Motion

A disc rotates in a horizontal plane with 360 revolutions per minute

At a distance of 20 cm from the center is a block with a mass of 100 g.

frequency f =  360 rev/minute =6 rev /second       f = 6 Hz

period   T=1/f = 1/6 = 0.17 s

speed  of the block   v = (2 π r) / T = (2 π 0.20)/0.17 = 7.39 m/s

angular velocity  ω = (2 π) / r = (2 π) /0.20 = 31.4 rad/s

centripetal acceleration  of the block   ac = v2/r = 7.392/0.20 = 2.73 x 102 ms-2

Remark

 In an uniform circular motion is the speed constant

The acceleration is directed toward the center of the circular path. This causes a change in direction of the velocity. The speed (magnitude of the velocity) does not change. 

(Centripetal Force : see chapter Force and Torque)  

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