A solid disk, spinning counter-clockwise, has a mass of #15 kg# and a radius of #6 m#. If a point on the edge of the disk is moving at #2 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?
Angular momentum is given by
The moment of inertia of a solid disk is given by
We are given that
This is the angular velocity. Note this is a positive quantity as the disk spins counter-clockwise, which by convention is the positive direction.
Note: The radian is a defined unit. It's definition of a ratio of two lengths makes it a pure number without dimensions. The unit of angle, be it radians, degrees, or revolutions, is really just a name to remind us that we're dealing with angle. Consequently, the radian unit seems to appear or disappear without warning. Above we have velocity divided by distance, which we would expect to have units of
This is the moment of inertia.
We can now calculate the angular momentum:
- Knight, R. D. In Physics for Scientists and Engineers ; Houston, A., Ed.; Pearson: Glenview, IL, 2013; pp 99, 102.