How a DVD player works
Information is encoded on a DVD in the form of small uniformly spaced
pits on a long arithmetic spiral starting close to the center and spiraling
out to the outer edge of the disk.
A laser reading head moves from near the center along a radius
toward the outer edge.
If the disk turns at a constant angular velocity, pits near
the center would pass under the reading head more slowly than pits
near the outer edge. In order for the DVD to be read properly, the angular velocity
of the disk must vary with the position of the reading head.
The right hand panel shows the relationship among the relevant quantities.
If the radius of the first pit is r, that of the last pit is R, the
angular velocity of the turning disk is f, derive an expression for
rate at which angular velocity of the disk varies with the position
of the reading head.