A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $12 c m$ $12 cm$ , respectively, and a mass of $9 k g$ $9 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $1 H z$ $1 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-05-14T11:48:34

The change in angular momentum is $= 7.63 k g m^{2} s^{- 1}$ $=7.63kgm^2s^-1$

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

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

Mass, $m = 9 k g$ $m=9kg$

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

So, $I = 9 \cdot \frac{({0.09}^{2} + {0.12}^{2})}{2} = 0.2025 k g m^{2}$ $I=9*((0.09^2+0.12^2))/2=0.2025kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

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

The change in angular momentum is

$DeltaL=0.2025*12pi=7.63kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 12 cm12cm12 cm, respectively, and a mass of 9 kg9kg9 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 1 Hz1Hz1 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?