An old-fashioned single-play vinyl record rotates on a turntable at 45.0 rpm. what are (a) the angular velocity in rad/s and (b) the period of the motion?

Part (a)

The rotational speed is

ω = (45 rev/min)

= (45 rev/min) * (2π rad/rev) * (1/60 min/s)

= (3π) / 2 rad/s = 4.71 rad/s

Answer: (3/2) π rad/s or 4.71 rad/s

Part (b)

The period, T, is related to angular velocity by

ω = (2π) / T, or

T = (2π) / ω

= (2π) / (1.5π rad/s)

= 4/3 s or 1.333 s

Answer: 4/3 s or 1.333 s