A cylinder has inner and outer radii of 4 cm and 8 cm, respectively, and a mass of 3 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?

Mar 8, 2017

The change in angular momentum is $= 0.38 k g {m}^{2} {s}^{-} 1$

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, $I = 3 \cdot \frac{{0.04}^{2} + {0.08}^{2}}{2} = 0.012 k g {m}^{2}$

The change in angular momentum is

$\Delta L = I \Delta \omega$

The change in angular velocity is

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

The change in angular momentum is

$\Delta L = 0.012 \cdot 10 \pi = 0.38 k g {m}^{2} {s}^{-} 1$