A cylinder has inner and outer radii of $4 c m$ $4 cm$ and $5 c m$ $5 cm$ , respectively, and a mass of $5 k g$ $5 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $12 H z$ $12 Hz$ to $9 H z$ $9 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-09-13T05:29:48

The change in angular momentum is $= 0.19 k g m^{2} s^{- 1}$ $=0.19kgm^2s^-1$

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

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

and $ω$ $omega$ is the angular velocity

The mass of the cylinder is $m = 5 k g$ $m=5kg$

The radii of the cylinder are $r_{1} = 0.04 m$ $r_1=0.04m$ and $r_{2} = 0.05 m$ $r_2=0.05m$

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, $I = 5 \cdot \frac{{0.04}^{2} + {0.05}^{2}}{2} = 0.01025 k g m^{2}$ $I=5*(0.04^2+0.05^2)/2=0.01025kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(12-9)*2pi=6pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.01025*6pi=0.19kgm^2s^-1$

A cylinder has inner and outer radii of 4 cm4cm4 cm and 5 cm5cm5 cm, respectively, and a mass of 5 kg5kg5 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12Hz12 Hz to 9 Hz9Hz9 Hz, by how much does its angular momentum change?