Question 740: Centre of Mass and Rotational Motion

Question

A disc of mass $M$ and radius $R$ is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass $M$ and radius $R / 2$ is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed $\omega$. If the angular speed at which the large disc rotates is $\omega / n$, then the value of $n$ is ___________.

Accepted Answer

On applying conservation of angular momentum about axis of larger disc.
$$\begin{aligned}
& \frac{1}{2} \cdot M\left(\frac{R}{2}ight)^2 \cdot \omega-M\left(\omega^{\prime} Right) \cdot R-\frac{M R^2}{2} \cdot \omega^{\prime}=0 \
& \Rightarrow \frac{\omega}{8}=\frac{3 \omega^{\prime}}{2} \
& \Rightarrow \omega^{\prime}=\frac{\omega}{12} \quad 	ext { Hence, } \mathrm{n}=12
\end{aligned}$$

Centre of Mass and Rotational Motion

Integer / Numeric Answer Type