A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $16 c m$ $16 cm$ , respectively, and a mass of $6 k g$ $6 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $9 H z$ $9 Hz$ to $3 H z$ $3 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-06-14T05:54:02

The change in angular momentum is $= 3.81 k g m^{2} s^{- 1}$ $=3.81kgm^2s^-1$

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

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

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, $I = 6 \cdot \frac{({0.09}^{2} + {0.16}^{2})}{2} = 0.1011 k g m^{2}$ $I=6*((0.09^2+0.16^2))/2=0.1011kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

The change in angular velocity is

$Delta omega=(9-3)*2pi=(12pi)rads^-1$

The change in angular momentum is

$DeltaL=0.1011*12pi=3.81kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 16 cm16cm16 cm, respectively, and a mass of 6 kg6kg6 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 9 Hz9Hz9 Hz to 3 Hz3Hz3 Hz, by how much does its angular momentum change?