A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $16 c m$ $16 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $19 H z$ $19 Hz$ to $18 H z$ $18 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-05-22T18:27:13

THe change in angular momentum is $= 0.42 k g m^{2} s^{- 1}$ $=0.42kgm^2s^-1$

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

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

Mass, $m = 4 k g$ $m=4kg$

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

So, $I = 4 \cdot \frac{({0.09}^{2} + {0.16}^{2})}{2} = 0.0674 k g m^{2}$ $I=4*((0.09^2+0.16^2))/2=0.0674kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(19-18)*2pi=(2pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0674*2pi=0.42kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 16 cm16cm16 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 19 Hz19Hz19 Hz to 18 Hz18Hz18 Hz, by how much does its angular momentum change?