A wheel of radius 14 inches is rotating 0.5 rad/s. what is the linear speed v, the angular speed in rpm, and the angular speed in deg/s?

First, let us find for the linear speed v. The formula for this is:

v = r w

where r is radius and w is radial velocity, therefore the linear speed is:

v = 14 inches (0.5 rad / s)

v = 7 inches / s

Now calculating for angular speed in rpm or revolutions per minute:

angular speed in rpm = (0.5 rad / s) (1 rev / 2π rad) (60 s / min)

angular speed in rpm = (15/π) rpm = 4.77 rpm

Finally calculating for angular speed in deg per second:

angular speed in rpm = (0.5 rad / s) (360° / 2π rad)

angular speed in rpm = (90/π) deg/s = 28.65 deg/s