Question 562: Centre of Mass and Rotational Motion

Question

A disc has mass $$M$$ and radius $$R$$. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity '$$\omega$$' in time $$\mathrm{t}$$ ?

Accepted Answer

Torque: $$	au=\mathrm{I} \alpha=\frac{\mathrm{MR}^2}{2} 	imes \frac{\omega}{\mathrm{t}}$$
$$\begin{array}{ll}
	herefore \quad & 	au=\frac{\mathrm{MR}^2 \omega}{2 \mathrm{t}} \
& 	ext { But } 	au=\mathrm{R} 	imes \mathrm{F} \
	herefore \quad & \mathrm{F}=\frac{	au}{\mathrm{R}}=\frac{\mathrm{MR} \omega}{2 \mathrm{t}}
\end{array}$$

Answer

$$\frac{M R \omega}{4 t}$$

Answer

$$\frac{\mathrm{MR} \omega}{2 \mathrm{t}}$$

Answer

$$\frac{\mathrm{MR} \omega}{\mathrm{t}}$$

Answer

$$\mathrm{MR} \omega \mathrm{t}$$

Centre of Mass and Rotational Motion

A disc has mass $M and radius R. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity '\omega' in time \mathrm{t}$ ?

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