Final answer:
To find the angular distance traveled by a piece of dust on a CD spinning at 440 rpm for 2.9 minutes, convert the spin rate to rad/s, time to seconds, and use the formula for angular distance θ = ωt.
Step-by-step explanation:
The student has asked about the angular distance a piece of dust on a CD would travel given that the CD spins at a constant rate of 440 rpm for a duration of 2.9 minutes.
To answer this question, we first need to convert the spin rate from revolutions per minute (rpm) to radians per second, as the SI unit for angular velocity is rad/s. Then, we can calculate the angular distance using the formula θ = ωt, where θ is the angular distance in radians, ω is the angular velocity in rad/s, and t is the time in seconds.
Step-by-step calculation
Convert the spin rate from rpm to rad/s: ω = 440 rpm * (2π rad/1 rev) * (1 min/60 s).
Convert time from minutes to seconds: t = 2.9 min * 60 s/min.
Calculate the angular distance: θ = ωt.
Following the steps above will yield the angular distance in radians that the piece of dust travels in 2.9 minutes.