# A cylinder has inner and outer radii of 2 cm and 4 cm, respectively, and a mass of 15 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 3 Hz to 7 Hz, by how much does its angular momentum change?

Feb 5, 2018

The change in angular momentum is $= 0.38 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

and $\omega$ is the angular velocity

The mass of the cylinder is $m = 15 k g$

The radii of the cylinder are ${r}_{1} = 0.02 m$ and ${r}_{2} = 0.04 m$

For the cylinder, the moment of inertia is $I = m \frac{\left({r}_{1}^{2} + {r}_{2}^{2}\right)}{2}$

So, $I = 15 \cdot \frac{\left({0.02}^{2} + {0.04}^{2}\right)}{2} = 0.015 k g {m}^{2}$

The change in angular velocity is

$\Delta \omega = \Delta f \cdot 2 \pi = \left(7 - 3\right) \times 2 \pi = 8 \pi r a {\mathrm{ds}}^{-} 1$

The change in angular momentum is

$\Delta L = I \Delta \omega = 0.015 \times 8 \pi = 0.38 k g {m}^{2} {s}^{-} 1$