A disc is rolling (without slipping) on a hor | vedclass

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Question

(A) rolling motion can be considered as a combination of pure translation of the centre of mass $C$ with velocity $V_C = R\omega$ and pure rotation ab

Vedclass · Accepted Answer

$V_Q > V_C > V_P$

Vedclass · Answer

(A) rolling motion can be considered as a combination of pure translation of the centre of mass $C$ with velocity $V_C = R\omega$ and pure rotation about the centre $C$ with angular velocity $\omega$. For any point at a distance $r$ from the centre $C$,the velocity due to rotation is $v_{rot} = r\omega$. The velocity of any point is the vector sum of the translational velocity $\vec{V}_C$ and the rotational velocity $\vec{v}_{rot}$. For points $P$ and $Q$ on the horizontal diameter: $1$. At point $Q$,the rotational velocity is in the same direction as the translational velocity. Thus,$V_Q = V_C + r\omega = R\omega + r\omega = (R+r)\omega$. $2$. At point $P$,the rotational velocity is in the opposite direction to the translational velocity. Thus,$V_P = |V_C - r\omega| = |R\omega - r\omega| = (R-r)\omega$. Since $R > r$,we have $V_Q > V_C > V_P$.

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