A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $11 c m$ $11 cm$ , respectively, and a mass of $5 k g$ $5 kg$ . 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 · 2018-01-04T07:36:45

The change in angular momentum is $= 1.587 k g m^{2} s^{- 1}$ $=1.587kgm^2s^-1$

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

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

and $ω$ $omega$ is the angular velocity

The mass of the cylinder is $m = 5 k g$ $m=5kg$

The radii of the cylinder are $r_{1} = 0.09 m$ $r_1=0.09m$ and $r_{2} = 0.11 m$ $r_2=0.11m$

For the cylinder, the moment of inertia is $I = m \frac{(r_{1}^{2} + r_{2}^{2})}{2}$ $I=m((r_1^2+r_2^2))/2$

So, $I = 5 \cdot \frac{({0.09}^{2} + {0.11}^{2})}{2} = 0.0505 k g m^{2}$ $I=5*((0.09^2+0.11^2))/2=0.0505kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(12-7) xx2pi=10pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.0505 xx10pi=1.587kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 11 cm11cm11 cm, respectively, and a mass of 5 kg5kg5 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?