1. Calculate the angular speed of the 26-inch bicycle rotating at 200 revolutions per minute. Express your answer in radians per minute. Use π = 3.14. Round to the nearest whole number.
2. Next, calculate the linear speed of the 26-inch bicycle being pedaled at a rate of 200 revolutions per minute. Express your answer in inches per minute rounded to the nearest whole number. (Hint: The diameter of the wheel is 26 inches.)
3. Expressing a speed in inches per minute has very little meaning in the context of the problem. It would be more useful to express the answer in miles per hour. Use dimensional analysis procedures to transform your answer from problem 3 into miles per hour, rounded to the nearest tenth.
4. Use your answers to problems 2-4 to calculate the linear speed, in miles per hour, of a 20-inch bicycle being pedaled at a rate of 200 revolutions per minute. Round to the nearest tenth.
5. Suppose you are riding the 20-inch bike illustrated in this set of problems, and a friend is riding the 26-inch bike. Assuming that your friend is pedaling the 26-inch bike at a rate of 200 revolutions per minute; will you have to pedal the 20-inch bike faster or slower than 200 revolutions per minute for you and your friend to be riding at the same speed? Explain your answer in terms of angular and linear velocity.
6. At what rate would you have to pedal a 20-inch bike so that it traveled at a linear speed of 15.5 miles per hour? Express you answer in revolutions per minute rounded to the nearest whole number. (Hint: First change miles per hour into inches per minute.)