A cyclist is riding a bicycle whose wheels have a diameter o

A cyclist is riding a bicycle whose wheels have a diameter of 24 inches.Suppose the wheels turn at a rate of 270 revolutions per minute. a) find the angular speed of the wheels in radians per minute. b) find the speed of the cyclist in miles per hour. use the fact that 1 mi =5280ft. do not round any intermediate computations, and round your answer to the nearest whole number.

Solution

1 mi = 5280 ft

diameter of wheel = 24 inches

angular speed = revolutions / minute * 2pi radians / revolutions = 270 * 2pi = 1695.6 radians / minute

b) circumference of wheel = 24pi inches

linear speed = 1695.6 * 12 = 20347.2 inches / minute = 19.268 miles / hour