The rear wheel of a tractor has a 24 inch radius. If it is traveling at 20 miles/hour, what is the angular speed of the wheel? What is the angle through which it rotates in 15 seconds?

Answer 1

Given

r = 24 in

V = 20 miles/hr * 63360 in/mile * 1 hr / 3600 seconds = 351.9 in/s

Solution

V = w * r

w = V/r = 351.9 / 24 = 14.66 rad/s

w = θ / t

θ = w * t = 14.66 * 15 = 219.9 rad

θ = 219.9 (180/π) = 12,600.3 degrees