Please help...a computerized spin balance machine rotates a 25 inch diameter tire at 480 revolutions per minute. (a) find the road speed in miles per hour at which the tire is being balanced (b) at what rate should the spin balance machine be set so that the tire is being tested for 70 miles per hour?

Answer 1

one rotation covers 25π inches
so in 1 minute it covers 12000π inches
and in 1 hour it covers 720000π inches

1 mile = 5280 ft = 63360 inches

so it goes 720000π/63360 miles/hour = 35.7 mph

since the road speed varies directly with the rmp

35.7/480 = 70/x
35.7x = 33600
x = 33600/35.7 = appr 941 rpm