A cylinder has inner and outer radii of $5 c m$ $5 cm$ and $8 c m$ $8 cm$ , respectively, and a mass of $3 k g$ $3 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $12 H z$ $12 Hz$ to $4 H z$ $4 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2018-03-25T06:54:45

The change in angular momentum is $= 0.67 k g m^{2} s^{- 1}$ $=0.67kgm^2s^-1$

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

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

and $ω$ $omega$ is the angular velocity

The mass of the cylinder is $m = 3 k g$ $m=3kg$

The radii of the cylinder are $r_{1} = 0.05 m$ $r_1=0.05m$ and $r_{2} = 0.08 m$ $r_2=0.08m$

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

So, $I = 3 \cdot \frac{({0.05}^{2} + {0.08}^{2})}{2} = 0.01335 k g m^{2}$ $I=3*((0.05^2+0.08^2))/2=0.01335kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(12-4) xx2pi=16pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.01335xx16pi=0.67kgm^2s^-1$

A cylinder has inner and outer radii of 5 cm5cm5 cm and 8 cm8cm8 cm, respectively, and a mass of 3 kg3kg3 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12Hz12 Hz to 4 Hz4Hz4 Hz, by how much does its angular momentum change?