A cylinder has inner and outer radii of $5 c m$ $5 cm$ and $11 c m$ $11 cm$ , respectively, and a mass of $5 k g$ $5 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $12 H z$ $12 Hz$ to $6 H z$ $6 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-07-25T11:07:31

The change in angular momentum is $= 1.376 k g m^{2} s^{- 1}$ $=1.376kgm^2s^-1$

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

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

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

So, $I = 5 \cdot \frac{{0.05}^{2} + {0.11}^{2}}{2} = 0.0365 k g m^{2}$ $I=5*(0.05^2+0.11^2)/2=0.0365kgm^2$

The change in angular velocity is

$Delta omega=(12-6)*2pi=12pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega$

$=0.0365*12pi=1.376kgm^2s^-1$

A cylinder has inner and outer radii of 5 cm5cm5 cm and 11 cm11cm11 cm, respectively, and a mass of 5 kg5kg5 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12Hz12 Hz to 6 Hz6Hz6 Hz, by how much does its angular momentum change?