A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $12 c m$ $12 cm$ , respectively, and a mass of $2 k g$ $2 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $24 H z$ $24 Hz$ to $18 H z$ $18 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-06-02T12:20:47

The change in angular momentum is $= 0.85 k g m^{2} s^{- 1}$ $=0.85kgm^2s^-1$

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

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

Mass, $m = 2 k g$ $m=2kg$

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

So, $I = 2 \cdot \frac{({0.09}^{2} + {0.12}^{2})}{2} = 0.0225 k g m^{2}$ $I=2*((0.09^2+0.12^2))/2=0.0225kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(24-18)*2pi=(12pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0225*12pi=0.85kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 12 cm12cm12 cm, respectively, and a mass of 2 kg2kg2 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 24 Hz24Hz24 Hz to 18 Hz18Hz18 Hz, by how much does its angular momentum change?