A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $16 c m$ $16 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $19 H z$ $19 Hz$ to $15 H z$ $15 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-08-22T14:57:25

The change in angular momentum is $= 1.69 k g m^{2} s^{- 1}$ $=1.69kgm^2s^-1$

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

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

The mass of the cylinder is $m = 4 k g$ $m=4kg$

The radii of the cylinder are $r_{1} = 0.09 m$ $r_1=0.09m$ and $r_{2} = 0.16 m$ $r_2=0.16m$

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, $I = 4 \cdot \frac{{0.09}^{2} + {0.16}^{2}}{2} = 0.0674 k g m^{2}$ $I=4*(0.09^2+0.16^2)/2=0.0674kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(19-15)*2pi=8pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.0674*8pi=1.69kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 16 cm16cm16 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 19 Hz19Hz19 Hz to 15 Hz15Hz15 Hz, by how much does its angular momentum change?