Awoman rides a bicycle for 3 hours and travels 51 kilometers. find the angular velocity of the wheel if the radius is 30 centimeters

First step is to find the circumference of the wheel (pi x diameter)
The radius is half of the diameter so 2 x 30 = 60
60 x pi (3.14) = 188.4 centimeters or 1.884 meters

Changing the kilometers into meters, and diving by 3 (to reduce the 3 hours into meter per hour) you'd get the total distance covered is 36,000 meters which equates to 12,000/hour or 200 meters/minute or 3.33 meters/second.

You take 3.33 and divide it by 1.884 which will give you 1.7675
Now you multiply it by the number of degrees of the wheel (which of course is 360) so 1.7675 x 360 = 636.3

Your answer is 636.3 degrees per second.