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 10 Hz to 15 Hz, by how much does its angular momentum change?

Feb 16, 2017

The change in angular momentum is $= 2.122 .12 k g {m}^{2} {s}^{- 1}$

Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

The change in angular momentum is

$\Delta L = I \cdot \Delta \omega$

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

$\Delta \omega = \left(15 - 10\right) \cdot 2 \pi = \left(10 \pi\right) r a {\mathrm{ds}}^{-} 1$

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

$L = 10 \pi \cdot 0.0674 = 2.12 k g {m}^{2} {s}^{- 1}$