Information is encoded on a DVD in the form of small uniformly spaced[br]pits on a long arithmetic spiral starting close to the center and spiraling [br]out to the outer edge of the disk.[br][br]A laser reading head moves from near the center along a radius[br]toward the outer edge.[br][br]If the disk turns at a constant angular velocity, pits near[br]the center would pass under the reading head more slowly than pits [br]near the outer edge. In order for the DVD to be read properly, the angular velocity[br]of the disk must vary with the position of the reading head.[br][br]The right hand panel shows the relationship among the relevant quantities.[br]If the radius of the first pit is [i][b][size=150]r[/size][/b][/i], that of the last pit is [i][b][size=150]R[/size][/b][/i], the [br]angular velocity of the turning disk is[size=150][i][b] f[/b][/i][/size], derive an expression for [br]rate at which angular velocity of the disk varies with the position[br]of the reading head.