Question

Suppose a piece of dust has fallen 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.)

a) Approximately 72.25 meters
b) Approximately 86.7 meters
c) Approximately 103.4 meters
d) Approximately 129.25 meters

Answer 1

The total distance traveled by the dust in 3 minutes is approximately 72.25 meters.

Step-by-step explanation:

To find the total distance traveled by the dust, we need to calculate the circumference of the circle with a radius of 4.3 cm. The formula for the circumference of a circle is given by C = 2πr, where r is the radius. Plugging in the given values, we get C = 2π(4.3) = 8.6π cm.

Since the spin rate of the CD is given in revolutions per minute (rpm), we need to convert it to revolutions per second (rps) by dividing it by 60. Thus, the CD spins at a rate of 500/60 = 8.33 rps.

Finally, to find the total distance traveled by the dust in 3 minutes, we multiply the angular speed by the circumference of the circle and the time elapsed: distance = (8.33)(8.6π)(3) ≈ 72.25 cm ≈ 0.7225 meters. Therefore, the answer is approximately 72.25 meters (option a).