A cylinder has inner and outer radii of $2 c m$ $2 cm$ and $4 c m$ $4 cm$ , respectively, and a mass of $15 k g$ $15 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $3 H z$ $3 Hz$ to $2 H z$ $2 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-09-08T06:19:04

The change in angular momentum is $= 0.094 k g m^{2} s^{- 1}$ $=0.094kgm^2s^-1$

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

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

The mass of the cylinder is $m = 15 k g$ $m=15kg$

The radii of the cylinder are $r_{1} = 0.02 m$ $r_1=0.02m$ and $r_{2} = 0.04 m$ $r_2=0.04m$

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

So, $I = 15 \cdot \frac{{0.02}^{2} + {0.04}^{2}}{2} = 0.015 k g m^{2}$ $I=15*(0.02^2+0.04^2)/2=0.015kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(3-2)*2pi=2pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.015*2pi=0.094kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 4 cm4cm4 cm, respectively, and a mass of 15 kg15kg15 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 3 Hz3Hz3 Hz to 2 Hz2Hz2 Hz, by how much does its angular momentum change?