A cylinder has inner and outer radii of $16 c m$ $16 cm$ and $21 c m$ $21 cm$ , respectively, and a mass of $2 k g$ $2 kg$ . If the cylinder's frequency of rotation about its center changes from $4 H z$ $4 Hz$ to $9 H z$ $9 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-02-25T18:17:28

The change in angular momentum $= 2.19 k g m^{2} s^{- 1}$ $=2.19kgm^2s^-1$

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

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

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

So, $I = 2 \cdot \frac{{0.16}^{2} + {0.21}^{2}}{2} = 0.0697 k g m^{2}$ $I=2*(0.16^2+0.21^2)/2=0.0697kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

$Delta omega=(9-4)*2pi=10pirads^-1$

$DeltaL=0.0697*10pi=2.19kgm^2s^-1$

A cylinder has inner and outer radii of 16 cm16cm16 cm and 21 cm21cm21 cm, respectively, and a mass of 2 kg2kg2 kg. If the cylinder's frequency of rotation about its center changes from 4 Hz4Hz4 Hz to 9 Hz9Hz9 Hz, by how much does its angular momentum change?