A cylinder has inner and outer radii of $5 c m$ $5 cm$ and $9 c m$ $9 cm$ , respectively, and a mass of $8 k g$ $8 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $15 H z$ $15 Hz$ to $7 H z$ $7 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-01-21T14:11:39

The answer is $= 2.131 k g m s^{- 1}$ $=2.131kgms^-1$

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

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

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

So, $I = 8 \cdot \frac{({(0.09)}^{2} + {(0.05)}^{2})}{2} = 4 \cdot 0.0106 = 0.0424 k g m^{2}$ $I=8*(((0.09)^2+(0.05)^2))/2=4*0.0106=0.0424kgm^2$

$L_{1} = 0.0424 \cdot 15 \cdot 2 π = 3.996 k g m s^{- 1}$ $L_1=0.0424*15*2pi=3.996kgms^(-1)$

$L_{2} = 0.0424 \cdot 7 \cdot 2 π = 1.865 k g m s^{- 1}$ $L_2=0.0424*7*2pi=1.865kgms^-1$

$DeltaL=L_1-L_2=3.996-1.865=2.131kgms^-1$

A cylinder has inner and outer radii of 5 cm5cm5 cm and 9 cm9cm9 cm, respectively, and a mass of 8 kg8kg8 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15Hz15 Hz to 7 Hz7Hz7 Hz, by how much does its angular momentum change?