A cylinder has inner and outer radii of $5 c m$ $5 cm$ and $9 c m$ $9 cm$ , respectively, and a mass of $8 k g$ $8 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $12 H z$ $12 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-05-08T12:26:44

The angular momentum changes by $= 1.33 k g m^{2} s^{- 1}$ $=1.33kgm^2s^-1$

The angular momentum is $L = I ω$ $L=Iomega$

where $I$ $I$ is the moment of inertia

Mass, $m = 8 k g$ $m=8kg$

For a cylinder, $I = m \frac{(r_{1}^{2} + r_{2}^{2})}{2}$ $I=m((r_1^2+r_2^2))/2$

So, $I = 8 \cdot \frac{({0.05}^{2} + {0.09}^{2})}{2} = 0.0424 k g m^{2}$ $I=8*((0.05^2+0.09^2))/2=0.0424kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(12-7)*2pi=(10pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0424*10pi=1.33kgm^2s^-1$

A cylinder has inner and outer radii of 5 cm5cm5 cm and 9 cm9cm9 cm, respectively, and a mass of 8 kg8kg8 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12Hz12 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?