# 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 4 Hz to 7 Hz, by how much does its angular momentum change?

Feb 1, 2017

The answer is $= 0.283 k g m {s}^{- 1}$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

$\Delta L = I \Delta \omega$

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

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

$\Delta \omega = \left(7 - 4\right) \cdot 2 \pi = 6 \pi r a {\mathrm{ds}}^{-} 1$

$\Delta L = 0.015 \cdot 6 \pi = 0.283 k g m {s}^{- 1}$