A cylinder has inner and outer radii of $12 c m$ $12 cm$ and $15 c m$ $15 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of rotation about its center changes from $2 H z$ $2 Hz$ to $8 H z$ $8 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2018-03-15T07:25:45

The change in angular momentum is $= 76.8 k g m^{2} s^{- 1}$ $=76.8kgm^2s^-1$

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 $m = 4 k g$ $m=4kg$

The radii of the cylinder are $r_{1} = 0.12 m$ $r_1=0.12m$ and $r_{2} = 0.15 m$ $r_2=0.15m$

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, $I = 4 \cdot \frac{({0.12}^{2} + {0.15}^{2})}{2} = 2.0369 k g m^{2}$ $I=4*((0.12^2+0.15^2))/2=2.0369kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(8-2) xx2pi=12pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=2.0369xx12pi=76.8kgm^2s^-1$

A cylinder has inner and outer radii of 12 cm12cm12 cm and 15 cm15cm15 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of rotation about its center changes from 2 Hz2Hz2 Hz to 8 Hz8Hz8 Hz, by how much does its angular momentum change?