A cylinder has inner and outer radii of $9 c m$ $9 cm$ 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 $5 H z$ $5 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2018-07-18T16:20:31

The change in angular momentum is $= 0.635 k g m^{2} s^{- 1}$ $=0.635kgm^2s^-1$

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

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

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

The mass of the cylinder is $m = 5 k g$ $m=5 kg$

The radii are $r_{1} = 0.09 m$ $r_1=0.09m$ and $r_{2} = 0.11 m$ $r_2=0.11m$

So, the moment of inertia is

$I = 5 \cdot \frac{{0.09}^{2} + {0.11}^{2}}{2} = 0.0505 k g m^{2}$ $I=5*(0.09^2+0.11^2)/2=0.0505kgm^2$

The change in angular velocity is

$Deltaomega=2pi(7-5)=4pirads^-1$

The change in angular momentum is

$DeltaL=IDeltaomega=0.0505*4pi=0.635kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 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 5 Hz5Hz5 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?