linear and angular motion

Question

A pulley driving a belt has a diameter of 360 mm and is turning at 2700/π revolutions per minute. Find the angular velocity of the pulley and the linear velocity of the belt assuming that no slip occurs.

Angular velocity ω = 2πn

n = 2700/60π revolutions per second

why is 2700/π ? and not (2 x π x 1500)/60

Answer 1

ω = 2 π N = 2 π (2700/π) = 5400 rad/sec

R = 360 mm/2 = .18 m

V = ω R = 5400 x .18 = 972 m/sec