A cylinder has inner and outer radii of $4 c m$ $4 cm$ and $8 c m$ $8 cm$ , respectively, and a mass of $3 k g$ $3 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $2 H z$ $2 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-06-23T06:00:01

The angular momentum changes by $= 0.38 k g m^{2} s^{- 1}$ $=0.38kgm^2s^-1$

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

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

The mass, $m = 3 k g$ $m=3kg$

For a cylinder, $I = m \frac{(r_{1}^{2} + r_{2}^{2})}{2}$ $I=m((r_1^2+r_2^2))/2$

So, $I = 3 \cdot \frac{({0.04}^{2} + {0.08}^{2})}{2} = 0.012 k g m^{2}$ $I=3*((0.04^2+0.08^2))/2=0.012kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(7-2)*2pi=(10pi)rads^-1$

The change in angular momentum is

$DeltaL=0.012*10pi=0.38kgm^2s^-1$

A cylinder has inner and outer radii of 4 cm4cm4 cm and 8 cm8cm8 cm, respectively, and a mass of 3 kg3kg3 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 2 Hz2Hz2 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?