Question

The drive motor of a particular CD player is controlled to rotate at a speed of 200 rpm when reading a track 5.7 centimeters from the center of the CD. The speed of the drive motor must vary so that the reading of data occurs at a constant rate.

a. Find the angular speed (in radians per minute) of the drive motor when it is reading a track 5.7 centimeters from the center of the CD.
b. Find the linear speed (in cm/sec) of a point on the CD that is 5.7 centimeters from the center of the CD.
C. Find the angular speed (in rpm) of the drive motor when it is reading a track 3 centimeters from the center of the CD. Remember the linear speed is the same for both tracks.

Answer 1

To find the angular speed of the drive motor and the linear speed of a point on the CD at a given radius.

Step-by-step explanation:

To find the angular speed of the drive motor when reading a track 5.7 centimeters from the center of the CD, we need to convert the speed from rpm to rad/min. Since 1 revolution is equal to 2π radians, we can calculate the angular speed using the formula: Angular Speed (in rad/min) = (Speed in rpm) x (2π radians/1 revolution) Substituting the given values, the angular speed is: Angular Speed = 200 rpm x (2π radians/1 revolution) For part (b), to find the linear speed of a point on the CD that is 5.7 centimeters from the center, we can use the formula for linear speed: Linear Speed (in cm/sec) = Angular Speed (in rad/min) x Radius (in cm)