A cylinder has inner and outer radii of $8 c m$ $8 cm$ and $15 c m$ $15 cm$ , respectively, and a mass of $3 k g$ $3 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $14 H z$ $14 Hz$ to $12 H z$ $12 Hz$ , by how much does its angular momentum change?

Question

1556 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-12T20:06:41

The change in angular momentum is $= 0.54 k g m^{2} s^{- 1}$ $=0.54kgm^2s^-1$

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

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

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

The radii of the cylinder are $r_{1} = 0.08 m$ $r_1=0.08m$ 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, $I = 3 \cdot \frac{{0.08}^{2} + {0.15}^{2}}{2} = 0.04335 k g m^{2}$ $I=3*(0.08^2+0.15^2)/2=0.04335kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(14-12)*2pi=4pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.04335*4pi=0.54kgm^2s^-1$

A cylinder has inner and outer radii of 8 cm8cm8 cm and 15 cm15cm15 cm, respectively, and a mass of 3 kg3kg3 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 14 Hz14Hz14 Hz to 12 Hz12Hz12 Hz, by how much does its angular momentum change?