A cylinder has inner and outer radii of $2 c m$ $2 cm$ and $12 c m$ $12 cm$ , respectively, and a mass of $2 k g$ $2 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $15 H z$ $15 Hz$ to $16 H z$ $16 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-02-28T18:49:52

The change in angular momentum is $= 0.093 k g m^{2} s^{- 1}$ $=0.093kgm^2s^-1$

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, $I = 2 \cdot \frac{{0.02}^{2} + {0.12}^{2}}{2} = 0.0148 k g m^{2}$ $I=2*(0.02^2+0.12^2)/2=0.0148kgm^2$

The change in angular momentum is

$DeltaL=IDelta omega$

$Delta omega=(16-15)*2pi=2pirads^-1$

$DeltaL=0.0148*2pi=0.093kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 12 cm12cm12 cm, respectively, and a mass of 2 kg2kg2 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15Hz15 Hz to 16 Hz16Hz16 Hz, by how much does its angular momentum change?