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 $15 H z$ $15 Hz$ to $8 H z$ $8 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-03-19T19:50:52

The change in angular momentum is $= 1.61 k g m^{2} s^{- 1}$ $=1.61kgm^2s^-1$

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

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(15-8)*2pi=(14pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0365*14pi=1.61kgm^2s^-1$

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 15 Hz15Hz15 Hz to 8 Hz8Hz8 Hz, by how much does its angular momentum change?