A cylinder has inner and outer radii of 13 cm and 15 cm, respectively, and a mass of 6 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 2 Hz to 3 Hz, by how much does its angular momentum change?

Jan 30, 2017

The answer is $= 0.74 k g m {s}^{- 1}$

Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

The change in angular momentum is

$\Delta L = I \Delta \omega$

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

So, $I = 6 \cdot \frac{{0.13}^{2} + {0.15}^{2}}{2} = 0.1182 k g {m}^{2}$

$\Delta \omega = \left(3 - 2\right) \cdot 2 \pi$

$\Delta L = 0.1182 \cdot 2 \pi = 0.74 k g m {s}^{- 1}$