Sample Questions

1. A 10" diameter wheel is spinning at 100 rpm. How fast is a point on the edge of the wheel moving?
2. Micah is driving 30 mph in his car. His car has tires that have a 24 inch diameter. How many revolutions per minute is the tire turning?
3. How many radians are in 200°?
4. How many degrees are in 10 radians?

Sample Response

1. One revolution = Circumference = 10*pi = 31.415 inches.
   So 100 rpm = 100 * 31.415 inches per minute.
   That's 3141.5 inches per minute.
   That's 261.8 feet per minute. (Divided by 12.)
   That's 15,707.5 feet per hour. (Multiplied by 60.)
   That's 2.97 miles per hour. (Divided by 5,280.)
   
   
2. One revolution = one circumference = 24*pi = 75.398 inches.
   30mph = 158,400 feet per hour. (Multiplied by 5,280.)
   That's 1,900,800 inches per hour. (Multiplied by 12.)
   That's 31,680 inches per minute. (Divided by 60.)
   That's about 420 rpm. (Divided by 75.398)
   
   
3. 180° = π radians.
   So using proportions we get
   
   
   
4. 180° = π radians.
   So using proportions we get