A computerized spin balance machine rotates a 35-inch-diameter tire at 400 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.)

(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.)

circumference = pi d = 110 inches = 9.16 feet

it does 400 circumferences /minute
9.16 ft * 400 = 3665 feet/minute

3665 feet/min * 60 min/hr * 1 mi/5280 ft
= 41.65 miles/hr

400 * (50/41.65) = 480.19 rpm

Thanks For your help with the 7 letter problem ! It was driving me crazy.

dang - go with Damon again. I used a 35" radius.

Note to self: read twice, type once.

To find the road speed at which the tire is being balanced, we can use the formula:

Road speed = circumference × RPM × conversion factor

(a) First, we need to find the circumference of the tire. The circumference of a circle is given by the formula:

Circumference = 2 × π × radius

Given that the diameter of the tire is 35 inches, we can calculate the radius by dividing it by 2:

Radius = 35 inches / 2 = 17.5 inches

Next, let's convert the radius from inches to miles. There are 5280 feet in a mile and 12 inches in a foot:

17.5 inches × 1 foot / 12 inches × 1 mile / 5280 feet = radius in miles

Now, we can find the circumference:

Circumference = 2 × π × radius = 2 × 3.14159 × radius in miles

Substituting the value of the radius in miles, we have:

Circumference = 2 × 3.14159 × (17.5 inches × 1 foot / 12 inches × 1 mile / 5280 feet)

Calculate the value of the circumference.

Next, we can substitute the values into the road speed formula:

Road speed = circumference × RPM × conversion factor

Substitute the value of the circumference and RPM (400) into the formula to calculate the road speed in miles per hour.

(b) To find the rate at which the spin balance machine should be set to test the tire at 50 miles per hour, we need to rearrange the road speed formula:

Rate = road speed / (circumference × conversion factor)

Substitute the values into the formula to calculate the rate at which the spin balance machine should be set.

Remember to round your answers to two decimal places, as instructed.

2π*35*400 = 28000π in/min

Now just convert that to mi/hr.

for 50mi/hr, just take the fraction needed to get 50. That is, if the answer to (a) is 100 mi/hr, just take 50/100 of 400rpm to get the balancing speed.