A wheel of radius 10 inches is rotating 45°/sec. What is the linear speed in in/sec and the angular speed in RPM? In/sec? RPM? What is the angular speed in radians/sec?

Question

It’s a two part question and we just started learning this and I’ve used this website as a reference because it really helps with the step-by-step process.

Answer 1

If it rotates at 45 degrees/sec then the angular speed is 45degrees/sec or (pi/8)radians /sec.

Since one revolution is 360 degrees or 2pi radiations it will take 8 seconds to go one revolution. 1 rev/8 sec is equivalent to 7.5 rev/min(7.5RPM)

Linear speed in radians/sec is (radius)x(angular speed)= 10(pi/8radians/sec)=10pi/8=5pi/4radians/sec