A cylinder has inner and outer radii of $4 c m$ $4 cm$ and $5 c m$ $5 cm$ , respectively, and a mass of $6 k g$ $6 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $7 H z$ $7 Hz$ to $12 H z$ $12 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-03-08T06:52:09

The change in angular momentum is $= 0.386 k g m^{2} s^{- 1}$ $=0.386kgm^2s^-1$

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

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

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

So, $I = 6 \cdot \frac{{0.04}^{2} + {0.05}^{2}}{2} = 0.0123 k g m^{2}$ $I=6*(0.04^2+0.05^2)/2=0.0123kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

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

The change in angular momentum is

$DeltaL=0.0123*10pi=0.386kgm^2s^-1$

A cylinder has inner and outer radii of 4 cm4cm4 cm and 5 cm5cm5 cm, respectively, and a mass of 6 kg6kg6 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 7 Hz7Hz7 Hz to 12 Hz12Hz12 Hz, by how much does its angular momentum change?