A CD has to rotate under the readout-laser with a constant linear velocity of 1.25 m/s. If the laser is at a position 3.2 cm from the center of the disk, what are the revolutions per minute (rpms) of the disk?

***Can someone please step me through the problem step by step?***

To solve this problem, you need to find the number of revolutions per minute (rpms) of the disk given the linear velocity and the distance of the laser from the center of the disk.

1. Start by converting the linear velocity from meters per second to centimeters per second, since the given distance is in centimeters. To do this, multiply the linear velocity by 100:
Velocity = 1.25 m/s * 100 = 125 cm/s

2. The circumference of a circle can be calculated using the formula: Circumference = 2πr, where r is the radius of the circle. In this case, the radius is given as 3.2 cm.

Circumference = 2π * 3.2 cm = 6.4π cm

3. Since the linear velocity is the distance traveled per unit time, you can find the distance traveled in one revolution by multiplying the circumference by the number of revolutions:
Distance per revolution = Circumference

4. Next, you need to convert the linear velocity to distance covered per minute. Since there are 60 seconds in a minute, you can multiply the linear velocity by 60:
Distance per minute = Velocity * 60

5. Now, you can calculate the number of revolutions per minute (rpms) by dividing the distance per minute by the distance per revolution:
rpms = Distance per minute / Distance per revolution

Plugging in the values:
rpms = (Velocity * 60) / Circumference

Substituting the known values:
rpms = (125 cm/s * 60) / (6.4π cm)

Finally, you can calculate the rpms using a calculator:
rpms ≈ 119.2

Therefore, the disk rotates at approximately 119.2 revolutions per minute (rpms).

The angular velocity required, in radians per second, is

w = V/R = 1.25/.032 = 39.1 rad/second

Multiply that by (60 s/min)*(1 rev/2 pi rad)
= 9.55 rpm/(rad/s)
for the rotation speed in rpm