A horizontal platform in the shape of a circular disk rotates freely in a horizo

Question

A horizontal platform in the shape of a circular disk rotates freely in a horizontal plane about a frictionless vertical axle. The platform has a massM= 100 kg and a radiusR=2.0m. A student whose mass ism=70kg walks slowly from the rim of the disk toward its center. If the angular speed of the system is3.0rad/s when the student is at the rim, what is the angular speed when she reaches a pointr=0.50m from the center?

Suppose the student had jumped on to the rim of the merry-go-round without transferring any angular momentum to the merry-go-round.

Explanation / Answer

a) as there is no change in angular momentum,

L = I will be constant.

before = after

MR2 /2 x + 0 = (MR2 /2 + mR2 )

(100 x 22 /2 ) x + 0 = (100 x 22 /2 + 70 x 22 ) x 3

200 = 480 x 3

= 7.2 rad/s

b) k.E = I2 /2 = [(100 x 22 /2 + 70 x 22 ) x 32 /2 ] - [(100 x 22 /2 ) x 7.22 /2 ]

              = 2160 - 5184 = - 3024 J

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