A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $14 c m$ $14 cm$ , respectively, and a mass of $9 k g$ $9 kg$ . If the cylinder's frequency of counterclockwise 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 · 2017-08-15T06:55:37

The change in angular momentum is $= 1.57 k g m s^{- 1}$ $=1.57kgms^-1$

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

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

The mass of the cylinder is $m = 9 k g$ $m=9kg$

The radii of the cylinder are $r_{1} = 0.09 m$ $r_1=0.09m$ and $r_{2} = 0.14 m$ $r_2=0.14m$

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

So, $I = 9 \cdot \frac{{0.09}^{2} + {0.14}^{2}}{2} = 0.12465 k g m^{2}$ $I=9*(0.09^2+0.14^2)/2=0.12465kgm^2$

The change in angular velocity is

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

The change in angular momentum is

$DeltaL=I Delta omega=0.12465*4pi=1.57kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 14 cm14cm14 cm, respectively, and a mass of 9 kg9kg9 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 5 Hz5Hz5 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?