A cylinder has inner and outer radii of $16 c m$ $16 cm$ and $24 c m$ $24 cm$ , respectively, and a mass of $3 k g$ $3 kg$ . If the cylinder's frequency of rotation about its center changes from $2 H z$ $2 Hz$ to $4 H z$ $4 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-10-26T11:18:13

The change in angular momentum is $= 1.57 k g m^{2} s^{- 1}$ $=1.57kgm^2s^-1$

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 $r_{1} = 0.16 m$ $r_1=0.16m$ and $r_{2} = 0.24 m$ $r_2=0.24m$

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, $I = 3 \cdot \frac{{0.16}^{2} + {0.24}^{2}}{2} = 0.1248 k g m^{2}$ $I=3*(0.16^2+0.24^2)/2=0.1248kgm^2$

The change in angular velocity is

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

The change in angular momentum is

$DeltaL=IDelta omega=0.1248 xx4pi=1.57kgm^2s^-1$

A cylinder has inner and outer radii of 16 cm16cm16 cm and 24 cm24cm24 cm, respectively, and a mass of 3 kg3kg3 kg. If the cylinder's frequency of rotation about its center changes from 2 Hz2Hz2 Hz to 4 Hz4Hz4 Hz, by how much does its angular momentum change?