A cylinder has inner and outer radii of $12 c m$ $12 cm$ and $15 c m$ $15 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of rotation about its center changes from $5 H z$ $5 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-08-20T06:17:33

The change in angular momentum is $= 0.93 k g m^{2} s^{- 1}$ $=0.93kgm^2s^-1$

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

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

The mass of the cylinder is $m = 4 k g$ $m=4kg$

The radii of the cylinder are $r_{1} = 0.12 m$ $r_1=0.12m$ and $r_{2} = 0.15 m$ $r_2=0.15m$

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

So, $I = 4 \cdot \frac{{0.12}^{2} + {0.15}^{2}}{2} = 0.0738 k g m^{2}$ $I=4*(0.12^2+0.15^2)/2=0.0738kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(7-5)*2pi=4pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.0738*4pi=0.93kgm^2s^-1$

A cylinder has inner and outer radii of 12 cm12cm12 cm and 15 cm15cm15 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of rotation about its center changes from 5 Hz5Hz5 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?