Rotational motion

Question

A disc of radius r = 20 cm is rotating about its axis with an angular speed of 20 rad s^{-1}. It is gently placed on a horizontal surface which is perfectly frictionless (Fig). What is the linear speed of point A on the disc (in m/s)?

Moderate

Solution

Since the surface is perfectly frictionless, the disc will not roll on the surface; it will simply keep on rotating at point B where it is placed. Now

Linear speed = distance from centre $\times $ angular speed

Given, $\mathrm{r}=20\mathrm{cm}=0.2\mathrm{m}\text{and}\mathrm{\omega}=20{\mathrm{rads}}^{-1}$

$\therefore $Linear speed at point $\mathrm{A}=\mathrm{OA}\times \mathrm{\omega}=\mathrm{r\omega}=0.2\times 20=4{\mathrm{ms}}^{-1}.$

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