# A cylinder has inner and outer radii of 5 cm and 9 cm, respectively, and a mass of 8 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz to 7 Hz, by how much does its angular momentum change?

May 8, 2017

The angular momentum changes by $= 1.33 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

Mass, $m = 8 k g$

For a cylinder, $I = m \frac{\left({r}_{1}^{2} + {r}_{2}^{2}\right)}{2}$

So, $I = 8 \cdot \frac{\left({0.05}^{2} + {0.09}^{2}\right)}{2} = 0.0424 k g {m}^{2}$

The change in angular momentum is

$\Delta L = I \Delta \omega$

The change in angular velocity is

$\Delta \omega = \left(12 - 7\right) \cdot 2 \pi = \left(10 \pi\right) r a {\mathrm{ds}}^{-} 1$

The change in angular momentum is

$\Delta L = 0.0424 \cdot 10 \pi = 1.33 k g {m}^{2} {s}^{-} 1$