# A cylinder has inner and outer radii of 9 cm and 16 cm, respectively, and a mass of 4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz to 18 Hz, by how much does its angular momentum change?

Aug 12, 2017

#### Answer:

The change in angular momentum is $= 2.54 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

The mass of the cylinder is $m = 4 k g$

The radii of the cylinder are ${r}_{1} = 0.09 m$ and ${r}_{2} = 0.16 m$

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

So, $I = 4 \cdot \frac{{0.09}^{2} + {0.16}^{2}}{2} = 0.0674 k g {m}^{2}$

The change in angular velocity is

$\Delta \omega = \Delta f \cdot 2 \pi = \left(18 - 12\right) \cdot 2 \pi = 12 \pi r a {\mathrm{ds}}^{-} 1$

The change in angular momentum is

$\Delta L = I \Delta \omega = 0.0674 \cdot 12 \pi = 2.54 k g {m}^{2} {s}^{-} 1$