A cylinder has inner and outer radii of $2 c m$ $2 cm$ and $4 c m$ $4 cm$ , respectively, and a mass of $12 k g$ $12 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $6 H z$ $6 Hz$ to $1 H z$ $1 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-11-11T06:36:24

The change in angular momentum is $= 0.38 k g m^{2} s^{- 1}$ $=0.38kgm^2s^-1$

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 $m = 12 k g$ $m=12kg$

The radii of the cylinder are $r_{1} = 0.02 m$ $r_1=0.02m$ and $r_{2} = 0.04 m$ $r_2=0.04m$

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, $I = 12 \cdot \frac{({0.02}^{2} + {0.04}^{2})}{2} = 0.012 k g m^{2}$ $I=12*((0.02^2+0.04^2))/2=0.012kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(6-1) xx2pi=10pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.012 xx10pi=0.38kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 4 cm4cm4 cm, respectively, and a mass of 12 kg12kg12 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 6 Hz6Hz6 Hz to 1 Hz1Hz1 Hz, by how much does its angular momentum change?