Question

A solid cylinder of mass, $m$, and radius, $r$, when rotating at an angular velocity, $\omega$ has an angular momentum $L$.
Which of the following would double the angular momentum of the cylinder?

• A. Doubling the mass of the cylinder while halving its angular velocity
• B. Doubling the angular velocity of the cylinder while having its mass
• C. Doubling the radius while halving the mass of the cylinder
• D. Quadrupling the mass while halving the radius of the cylinder
• E. Quadrupling the angular velocity while halving the radius of the cylinder

Answer 1

The correct option is C Doubling the radius while halving the mass of the cylinder

Moment of inertia of solid cylinder $I=\frac{1}{2}m{r}^2$

$\therefore$ Angular momentum $L=Iw=\frac{1}{2}m{r}^{2}w$ $⟹L\propto m{r}^{2}w$

Now for option C : $r^{\prime }=2r$ and $m^{\prime }=m/2$

$\therefore$ New angular momentum $L^{\prime }=\left(m/2\right)(2r{)}^{2}w=2m{r}^{2}w=2L$

Thus option C is correct.