A cylinder has inner and outer radii of $3 c m$ $3 cm$ and $9 c m$ $9 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $9 H z$ $9 Hz$ to $3 H z$ $3 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-12-01T07:09:22

The change in angular momentum is $= 0.68 k g m^{2} s^{- 1}$ $=0.68kgm^2s^-1$

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 $m = 4 k g$ $m=4kg$

The radii of the cylinder are $r_{1} = 0.03 m$ $r_1=0.03m$ and $r_{2} = 0.09 m$ $r_2=0.09m$

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, $I = 4 \cdot \frac{({0.03}^{2} + {0.09}^{2})}{2} = 0.018 k g m^{2}$ $I=4*((0.03^2+0.09^2))/2=0.018kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(9-3) xx2pi=12pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.018 xx12pi=0.68kgm^2s^-1$

A cylinder has inner and outer radii of 3 cm3cm3 cm and 9 cm9cm9 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 9 Hz9Hz9 Hz to 3 Hz3Hz3 Hz, by how much does its angular momentum change?