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Question

Suppose the platform with the kid in the previous problem is rotating in anticlockwise direction at an angular speed ω. The kid starts walking along the rim with a speed v relative to the platform also in the anticlockwise direction. Find the new angular speed of the platform.


Solution

From initial frame of reference when we see, the (man-wheel) system, we can find that the wheel moving with a speed of and the man with (w+vR) after the man has started walking.

(ω1= angular velocity after walking)

(ω= angular velocity of the wheel before walking.)

Since^^Ei = 0

extended torque = 0

Therefore,

(I+mR2)ω=Iω1+mR2(ω1+vR)

(I+mR2)ω=Iω1+mR2(ω1+vR)

(I+mR2)ωMvR

=(I+mR2)ω1

ω1=(I+MR2)ωMvR(I+MR2)

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