Consider a disc rotating in the horizontal pl | vedclass

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Question

(A) Let the position of the pebbles be defined by their distance $r$ from the center $O$. The angular velocity of a particle relative to the center is

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$P$ lands in the shaded region and $Q$ in the unshaded region

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(A) Let the position of the pebbles be defined by their distance $r$ from the center $O$. The angular velocity of a particle relative to the center is given by $\omega_{p} = \frac{v_{	heta}}{r}$,where $v_{	heta}$ is the tangential component of velocity. For pebble $P$,the distance $r$ from the center $O$ initially decreases as it moves towards $O$ and then increases after passing $O$. Since $v_{	heta}$ is constant,the angular velocity $\omega_{p} = \frac{v_{	heta}}{r}$ initially increases and then decreases. The average angular velocity of $P$ is greater than the angular velocity of the disc $\omega$. Thus,$P$ sweeps a larger angle than the disc and lands in the shaded region. For pebble $Q$,the distance $r$ from the center $O$ is continuously increasing as it moves away from $O$. Consequently,the angular velocity $\omega_{q} = \frac{v_{	heta}}{r}$ is continuously decreasing. The average angular velocity of $Q$ is less than the angular velocity of the disc $\omega$. Thus,$Q$ sweeps a smaller angle than the disc and lands in the unshaded region.

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