# A cylinder has inner and outer radii of 2 cm and 3 cm, respectively, and a mass of 1 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 6 Hz to 12 Hz, by how much does its angular momentum change?

Feb 18, 2017

The change in angular momentum is $= 0.0245 k g {m}^{2} {s}^{- 1}$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

and $\omega$ is the angular velocity

The change in angular momentum is

$\Delta L = I \Delta \omega$

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

So, $I = 1 \cdot \frac{{0.02}^{2} + {0.03}^{2}}{2} = 0.00065 k g {m}^{2}$

$\Delta \omega = \left(12 - 6\right) \cdot 2 \pi r a {\mathrm{ds}}^{-} 1$

$\Delta L = 0.00065 \cdot 12 \pi = 0.0245 k g {m}^{2} {s}^{- 1}$