A cylinder has inner and outer radii of $4 c m$ $4 cm$ and $5 c m$ $5 cm$ , respectively, and a mass of $6 k g$ $6 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $7 H z$ $7 Hz$ to $10 H z$ $10 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-07-09T06:00:44

The change in angular momentum is $= 0.23 k g m^{2} s^{- 1}$ $=0.23kgm^2s^-1$

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

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

The mass, $m = 6 k g$ $m=6kg$

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

So, $I = 6 \cdot \frac{({0.04}^{2} + {0.05}^{2})}{2} = 0.0123 k g m^{2}$ $I=6*((0.04^2+0.05^2))/2=0.0123kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(10-7)*2pi=(6pi)rads^-1$

The change in angular momentum is

$DeltaL=0.0123*6pi=0.23kgm^2s^-1$

A cylinder has inner and outer radii of 4 cm4cm4 cm and 5 cm5cm5 cm, respectively, and a mass of 6 kg6kg6 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 7 Hz7Hz7 Hz to 10 Hz10Hz10 Hz, by how much does its angular momentum change?