What's the constant angular speed of the wheel, & what's the linear speed of a point on the edge of the wheel?

Question

A beam of light passes through one of the slots at the outside edge of the wheel, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot in the wheel. One such slotted wheel has a radius of 5.0 cm and 500 slots around its edge. Measurements taken when the mirror is L = 500 m from the wheel indicate a speed of light of 3.0 x 10 ^5 km/s.
(A) What is the (constant) angular speed of the wheel?
(B) What is the linear speed of a point on the edge of the wheel?

The answers are:
(A) 3.8 x 10^ 3 rad/s
(B) 1.9 x 10^ 2 m/s


BUT I DON'T KNOW HOW TO GET THESE ANSWERS, AND I REALLY NEED HELP BECAUSE I HAVE A TEST NEXT WEEK. I REALLY WANT TO UNDERSTAND THIS, PLEASE HELP ME!

Answer 1

If the speed of light is calculated to be 3 x 10^5 km/s, and the light travels 1 km (2 times 500 m) while the wheel advances one slot, then we can calculate that it takes 1/3 x 10^-5 s (= 1 km / (3 x 10^5 km/s)) for the wheel to rotate a distance of one slot, which is 1/500 of a revolution.

To calculate revolutions per second, we have:
(1/500) revolution / (1/3 x 10^-5 x) = 600 revs/s

To convert to rad/s:
600 revs/s x 2 pi radians per revolution = 3770 rad/s
Rounding, we have 3800, or 3.8 x 10^3 rad/s

Since the radius of the wheel is 5 cm = 0.05 m, we have:
3.8 x 10^3 rad/s x 0.05 meters per radian =
190 m/s = 1.9 x 10^2 m/s