Question 253: Centre of Mass and Rotational Motion

Question

A solid circular disc of mass $$50 \mathrm{~kg}$$ rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \mathrm{~m} / \mathrm{s}$$. The absolute value of work done on the disc to stop it is ________ J.

Accepted Answer

Using work energy theorem
$$\begin{aligned}
& \mathrm{W}=\Delta \mathrm{KE}=0-\left(\frac{1}{2} \mathrm{mv}^2+\frac{1}{2} \mathrm{I} \omega^2ight) \
& \mathrm{W}=0-\frac{1}{2} \mathrm{mv}^2\left(1+\frac{\mathrm{K}^2}{\mathrm{R}^2}ight) \
& =-\frac{1}{2} 	imes 50 	imes 0.4^2\left(1+\frac{1}{2}ight)=-6 \mathrm{~J}
\end{aligned}$$
Absolute work $$=+6 \mathrm{~J}$$
$$W=-6 J \quad|W|=6 J$$

Centre of Mass and Rotational Motion

A solid circular disc of mass $50 \mathrm{~kg} rolls along a horizontal floor so that its center of mass has a speed of 0.4 \mathrm{~m} / \mathrm{s}$. The absolute value of work done on the disc to stop it is ________ J.

Integer / Numeric Answer Type