# A cylinder has inner and outer radii of 5 cm and 8 cm, respectively, and a mass of 3 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz to 4 Hz, by how much does its angular momentum change?

Mar 25, 2018

The change in angular momentum is $= 0.67 k g {m}^{2} {s}^{-} 1$

#### 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 $m = 3 k g$

The radii of the cylinder are ${r}_{1} = 0.05 m$ and ${r}_{2} = 0.08 m$

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

So, $I = 3 \cdot \frac{\left({0.05}^{2} + {0.08}^{2}\right)}{2} = 0.01335 k g {m}^{2}$

The change in angular velocity is

$\Delta \omega = \Delta f \cdot 2 \pi = \left(12 - 4\right) \times 2 \pi = 16 \pi r a {\mathrm{ds}}^{-} 1$

The change in angular momentum is

$\Delta L = I \Delta \omega = 0.01335 \times 16 \pi = 0.67 k g {m}^{2} {s}^{-} 1$