a. Assuming that the disk is free to slide on the ice, derive an expression for

Question

a. Assuming that the disk is free to slide on the ice, derive an expression for the speed of the disk and person immediately after the stone is thrown

b. Derive an expression for the time it will take the disk to stop sliding.

The person now stands on a similar disk that has a fixed pole through its centre, so that it can only rotate on the ice. The person throws the same stone (of mass m/20) horizontally in a tangential direction at initial speed v0, as shown in the figure below. The rotational inertia of the disk is (½) mR2.

c. Derive an expression for the angular speed ? of the disk immediately after the stone is thrown.

Explanation / Answer

a) Here, applying conservation of momentum

=> m/20 * vo =   (m + m/2) * v

=>   v = vo/30

=>   the speed of the disk and person immediately   = vo/30

b)     time it will take the disk to stop sliding = (vo/30)/g

                                                                    =   vo/(30g)

c) Applying conservation of angular momentum

=> (m/20) * vo * R   =   (1/2 * m * R2 + (m/2)R2) *

=>    =   vo/(20R)

=> angular speed of the disk immediately after the stone is thrown = vo/(20R)

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