A cylinder has inner and outer radii of $8 c m$ $8 cm$ and $15 c m$ $15 cm$ , respectively, and a mass of $3 k g$ $3 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $15 H z$ $15 Hz$ to $12 H z$ $12 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-07-20T05:36:15

The angular momentum changes by $= 0.82 k g m^{2} s^{- 1}$ $=0.82kgm^2s^-1$

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

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

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

So, $I = 3 \cdot \frac{{0.08}^{2} + {0.15}^{2}}{2} = 0.04335 k g m^{2}$ $I=3*(0.08^2+0.15^2)/2=0.04335kgm^2$

The change in angular velocity is

$Delta omega=(15-12)*2pi=6pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega$

$=0.04335*6pi=0.82kgm^2s^-1$

A cylinder has inner and outer radii of 8 cm8cm8 cm and 15 cm15cm15 cm, respectively, and a mass of 3 kg3kg3 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15Hz15 Hz to 12 Hz12Hz12 Hz, by how much does its angular momentum change?