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.
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)ω−MvR
=(I+mR2)ω1
⇒ω1=(I+MR2)ω−MvR(I+MR2)