Question

Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)

Answer 1

405.3m

Step-by-step explanation:

Since the CD spin rate is 500 rpm, or revolution per minutes, its angular speed in rad per second is

`\omega = 500 rev/min * 2\pi rad/rev * 1/60 min/sec = 52.36 rad/s`

The dusk is 4.3 cm from center, so its velocity must be

`v = R\omega = 4.3 * 52.36 = 225.14 cm/s`

Then the distance traveled by the dusk after 3 minutes, or 180 seconds is

`d = v*t = 225.14 * 180 = 40526.54 cm` or 405.3m