a wheel has a radius of 10 inches is rotating with an angula

a wheel has a radius of 10 inches is rotating with an angular velocity of 2.5 revolutions per second. Find the distance the wheel travels in 15 seconds. state the exact value and then round it off to three decimals?

Solution

Angular velocity = 2.5 rev/sec

Angular velocity in rad/sec = 2.5*2pi = 15.71 rad/sec

linear velocity = angular vel x radius = 15.71 x 10 = 157.1 inch/sec

Distance travelled in 15sec. = 15*157.1 = 2356.194 inches