Question

A solid disk, spinning counter-clockwise, has a mass of `2 kg` and a radius of `5/2 m`. If a point on the edge of the disk is moving at `15/4 m/s` in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Answer 1

Angular momentum `=9.375kg cdot m^2s^-1`
Angular velocity`=1.5radcdot s^-1`

Explanation:

For any object which is rotating about an axis, each point located on the object has the same angular velocity `omega`. Its units are `radcdot s^-1`. It can be found with the help of velocity `v` and radius `r` of a point using the relation

`omega=v/r`

Inserting given values we get
`omega=(15/4)/(5/2)`
`=>omega=(15/4)xx(2/5)=1.5radcdot s^-1`

The angular momentum `L` of a solid disc can be found using the following formula

`L = Ixxω`
where `I` is the moment of inertia of a solid disc and is given as `1/2Mr^2`. `M` being mass of disc.

If we substitute the value of `omega` in terms of `vand r`, the expression for angular momentum reduces to
`L = 1/2Mr^2xxv/r`
`=>L = 1/2Mrv`
Inserting given values
`L = 1/2xx2xx5/2xx15/4`
`=>L = 9.375kg cdot m^2s^-1`