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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion3 Marks
Question
Suppose the platform with the kid in the previous problem is rotating in anticlockwise direction at an angular speed $\omega.$ 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.
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Answer

From a inertial frame of reference when we see the (man wheel) system, we can find that the wheel moving at a speed of $\omega$ and the man with $\Big(\omega+\frac{\text{V}}{\text{R}}\Big)$ after the man has started walking. $(\omega'=$ angular velocity after walking, $\omega=$ angular velocity of the wheel before walking$).$ Since $\sum\text{l}=0$ Extended torque = 0 Therefore, $(1+\text{MR}^2)\omega=\text{l}\omega'+\text{mR}^2\Big(\omega'+\frac{\text{V}}{\text{R}}\Big)$ $\Rightarrow(1+\text{MR}^2)\omega=\text{l}\omega'+\text{mR}^2\omega'+\text{mVR}$ $\Rightarrow\omega'=\omega-\frac{\text{mVR}}{(1+\text{mR}^2)}.$

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