A cylinder has inner and outer radii of $2 c m$ $2 cm$ and $5 c m$ $5 cm$ , respectively, and a mass of $8 k g$ $8 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $6 H z$ $6 Hz$ to $4 H z$ $4 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-05-05T13:20:46

The change in angular momentum is $= 0.15 k g m^{2} s^{- 1}$ $=0.15kgm^2s^-1$

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, $I = 8 \cdot \frac{({0.02}^{2} + {0.05}^{2})}{2} = 0.0116 k g m^{2}$ $I=8*((0.02^2+0.05^2))/2=0.0116kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(6-4)*2pi=(4pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0116*4pi=0.15kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 5 cm5cm5 cm, respectively, and a mass of 8 kg8kg8 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 6 Hz6Hz6 Hz to 4 Hz4Hz4 Hz, by how much does its angular momentum change?