A cylinder has inner and outer radii of $8 c m$ $8 cm$ and $16 c m$ $16 cm$ , respectively, and a mass of $6 k g$ $6 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $9 H z$ $9 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-02-02T07:45:48

The answer is $= 1.21 k g m s^{- 1}$ $=1.21kgms^(-1)$

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

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

The change in angular momentum is

$DeltaL=IDelta omega$

$Delta omega$ is the change in angular velocity

For a cylinder, $I=m(r_1^2+r_2^2)/2$

So, $I=6*((0.08)^2+0.16^2)/2=0.096kgm^2$

$Delta omega=(9-7)*2pi=4pirads^-1$

$DeltaL=0.096*4pi=1.21kgms^(-1)$

A cylinder has inner and outer radii of 8 cm8cm8 cm and 16 cm16cm16 cm, respectively, and a mass of 6 kg6kg6 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 9 Hz9Hz9 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?