A computerized spin balance machine rotates a 35-inch-diameter tire at 420 revolutions per minute. (a) Find the road speed (in miles per hour) at which the tire is being balanced. (Round your answer to two decimal places.) mph (b) At what rate should the spin balance machine be set so that the tire is being tested for 50 miles per hour? (Round your answer to two decimal places.) revolutions per minute

Answer:

a) circumference = 35 π

Multiply revolutions per minute= 35 π × 420

= 46181.412 inches per minute

Convert to miles per minute =46181.412 /(12 × 5280) = 0.7288 miles per minute

Convert to miles per hour = (0.7288 × 60) miles per hour = 43.728 miles per hour

Therefore Road speed = 43.73 mph.

b) convert to miles per minute = (50 /60)miles per minute

=0.833 miles per minute.

Convert to inches per minute = (0.833 × 5280 × 12 ) inches per minute

= 52800 inches per minute.

Divide by circumference = (52800/35π) revolutions per minute

= 480. 44 revolutions per minute.