The angular speed is given as a function of the linear speed and radius as:
To find in radians per second, given that is in inches, we need to convert to inches per second:
My prof posted this problem as an example and, going over the steps, I haven't been able to work out how he got to the final answer.
A car has tires with 10 inch radius and is traveling at 60 miles per hour. Find the angular speed of the wheels in radians per second.
(60 miles/hr) = (60 miles/hr) * (5280 ft/1 mile) * (12 in/1 ft) * (2 pi rad/2 pi (10 in)) * (60 min/1 in) * (60 sec/1 min)
= 1.4*10^9 rad/sec
I'm not totally sure how he got to that final answer. When I tried it, I got something completely different. I'd appreciate a hint to the right direction.