Question

A cd has diameter of 130 millimeters. when playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. when reading along the outer edge of the disc, the angular speed is about 240 rpm (revolutions per minute). find the linear speed. round your answer to two decimal places. the linear speed of reading along the outer edge of the disc is number meters per second.

Answer 1

The linear speed of reading along the outer edge of the disc is approximately 5.95 m/s.

Step-by-step explanation:

To find the linear speed of reading along the outer edge of the disc, we need to first convert the given angular speed from revolutions per minute (rpm) to radians per second (rad/s).

Given that the angular speed is 240 rpm, we can convert this to rad/s using the following formula:

Angular speed (rad/s) = (angular speed in rpm) x (2π rad/1 min)

Plugging in the values, we get:

Angular speed (rad/s) = 240 rpm x (2π rad/1 min)

Next, we can calculate the linear speed using the formula:

Linear speed = (radius) x (angular speed)

Given that the diameter of the CD is 130 mm, the radius is half of that, which is 65 mm or 0.065 m

Plugging in the values, we get:

Linear speed = 0.065 m x (240 rpm x (2π rad/1 min))

Simplifying the expression, we get:

Linear speed = 0.065 m x (240 x 2π/60 rad/s)

Finally, we can compute the linear speed:

Linear speed = 0.065 m x (240 x 2π/60) rad/s

Round this answer to two decimal places, we get the linear speed of reading along the outer edge of the disc is approximately 5.95 m/s.