Question

What is the angular momentum of a gyroscope that is a solid cylinder with a radius of .24 m, a mass of 15 kg and a angular velocity of 140 rad/sec?

Answer 1

`vec L=Ixxvec omega`
or
`L=Ixxomega =60.48 kg m^2 s^-1`

Explanation:

The moment of inertia `I` for a solid cylinder is `1/2mr^2`.

Substitute into the equation `L=Ixxomega` to get;

`L=1/2mr^2omega`.

Crunch in the numbers and you should get `60.48kg m^2 s^-1`.

The formula for moment of inertia can be derived by exploiting the definition of moment of inertia, `I=ointr^2dm`.

Hope this helps. I would be happy to explain more on the derivation if you want. Cheers.