A cylinder has inner and outer radii of $2 c m$ $2 cm$ and $16 c m$ $16 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $10 H z$ $10 Hz$ to $15 H z$ $15 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-12-13T12:52:18

The change in angular momentum is $= 1.63 k g m^{2} s^{- 1}$ $=1.63kgm^2s^-1$

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 $r_{1} = 0.02 m$ $r_1=0.02m$ and $r_{2} = 0.16 m$ $r_2=0.16m$

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, $I = 4 \cdot \frac{({0.02}^{2} + {0.16}^{2})}{2} = 0.052 k g m^{2}$ $I=4*((0.02^2+0.16^2))/2=0.052kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(15-10) xx2pi=10pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.052 xx10pi=1.63kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 16 cm16cm16 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 10 Hz10Hz10 Hz to 15 Hz15Hz15 Hz, by how much does its angular momentum change?