A DVD is approximately 12 centimeters in diameter The drive

A DVD is approximately 12 centimeters in diameter. The drive motor of the DVD player is controlled to rotate precisely between 200 and 500 revolutions per minute, depending on what track is being read. (A). Find the interval for the angular speed of the a disc as it rotates (B). Find the linear speed of a point on the outermost track as the disc rotates.

Solution

Solution:

A)

As we know;

Each rotation corresponds to 2 radians,hence 200 revolutions per minute corresponds to (200)2 radians/minute and 500 revolutions per minute corresponds to (500)2 radians/minute.

i.e,

1256 rad/minute to 3140 rad/minute

B)

The linear speed is obtained by noting that one rotation corresponds to the circumference of the wheel. Hence the linear speed s is given by:

v(min) = 1256 rad/min × (radius) = 1256 × 6 cm/min => 7.536 metre/minute

v(max) = 3140 rad/min × (radius) = 3140  × 6 cm/min => 18.84 metre/minute