# A cylinder has inner and outer radii of 2 cm and 16 cm, respectively, and a mass of 9 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 10 Hz to 15 Hz, by how much does its angular momentum change?

##### 1 Answer
Feb 27, 2017

The change in angular momentum is $= 3.68 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

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

So, $I = 9 \cdot \frac{{0.02}^{2} + {0.16}^{2}}{2} = 0.117 k g {m}^{2}$

The change in angular momentum is

$\Delta L = I \Delta \omega$

$\Delta \omega = \left(15 - 10\right) \cdot 2 \pi = 10 \pi r a {\mathrm{ds}}^{-} 1$

$\Delta L = 0.117 \cdot 10 \pi = 3.68 k g {m}^{2} {s}^{-} 1$