A cylinder has inner and outer radii of $5 c m$ $5 cm$ and $9 c m$ $9 cm$ , respectively, and a mass of $5 k g$ $5 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $15 H z$ $15 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-06-06T12:19:16

The change in angular momentum is $= 1.33 k g m^{2} s^{- 1}$ $=1.33kgm^2s^-1$

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

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

Mass, $m = 5 k g$ $m=5kg$

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

So, $I = 5 \cdot \frac{({0.05}^{2} + {0.09}^{2})}{2} = 0.0265 k g m^{2}$ $I=5*((0.05^2+0.09^2))/2=0.0265kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(15-7)*2pi=(16pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0265*16pi=1.33kgm^2s^-1$

A cylinder has inner and outer radii of 5 cm5cm5 cm and 9 cm9cm9 cm, respectively, and a mass of 5 kg5kg5 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15Hz15 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?