The rear wheel of a tractor has a 24in radius Find the angle

The rear wheel of a tractor has a 24-in radius. Find the angle (in radians) through which a wheel rotates in 8 sec if the tractor is traveling at a speed of 21 mph. The wheel rotates through 123.20 radians. (Round to the nearest hundredth as needed.)

Solution

linear vel = radius*angular velocity

linear vel ( inch/sec) = 369.6 inch/sec

angular vel = 369.6/24 = 15.4 rad/sec

angle through which it rotates = (angular vel.)*time = 15.4*8 = 123.20 radians