A cylinder has inner and outer radii of $4 c m$ $4 cm$ and $18 c m$ $18 cm$ , respectively, and a mass of $1 k g$ $1 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $15 H z$ $15 Hz$ to $9 H z$ $9 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-07-26T14:17:30

The change in ngular momentum is $= 0.64 k g m^{2} s^{- 1}$ $=0.64kgm^2s^-1$

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

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

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

So, $I = 1 \cdot \frac{({0.04}^{2} + {0.18}^{2})}{2} = 0.017 k g m^{2}$ $I=1*((0.04^2+0.18^2))/2=0.017kgm^2$

The change in angular velocity is

$Delta omega=(15-9)*2pi=12pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega$

$=0.017*12pi=0.64kgm^2s^-1$

A cylinder has inner and outer radii of 4 cm4cm4 cm and 18 cm18cm18 cm, respectively, and a mass of 1 kg1kg1 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15Hz15 Hz to 9 Hz9Hz9 Hz, by how much does its angular momentum change?