The radius of each wheel of a car is 16 inches. At how many revolutions per minute should a spin balancer be set to balance the tires at a speed of 90 miles per hour? What is the setting for a wheel of radius 14 inches?
what happens to the 16 inches and 14 inches.
base figures you need to know
5280 feet in a mile
12 inches in a foot
60 minutes in an hour
The circumference of a circle formula is circumference = pi * radius * 2
the trick of this problem is you have feet in the mile but inches in the tire & hours in the speed but minutes in the revolutions
so you would have your speed (90) miles per hour divided by (60) minutes times the number of feet in a mile (5280) times number of inches in a foot (12) divided by the circumference of the tire pi * r2 (3.141593 * 16 * 2)
To determine the number of revolutions per minute (RPM) needed for the spin balancer, we can use the formula:
RPM = (speed in miles per hour * 5280 feet per mile) / (circumference of wheel in feet)
First, let's calculate the setting for a wheel with a radius of 16 inches:
1. Convert the speed of 90 miles per hour to feet per hour:
Speed in feet per hour = 90 miles per hour * 5280 feet per mile = 475,200 feet per hour.
2. Calculate the circumference of the wheel (diameter * π):
Circumference of the wheel = 2 * π * radius
= 2 * 3.14 * 16 inches
= 100.48 inches.
3. Convert the circumference of the wheel to feet:
Circumference in feet = 100.48 inches * (1 foot / 12 inches)
= 8.3733 feet.
4. Calculate the RPM:
RPM = 475,200 feet per hour / 8.3733 feet
≈ 56,782.95 revolutions per minute.
Therefore, the spin balancer should be set to approximately 56,783 RPM to balance the tires at a speed of 90 miles per hour.
Now, let's calculate the setting for a wheel with a radius of 14 inches:
1. Calculate the circumference of the wheel:
Circumference of the wheel = 2 * 3.14 * 14 inches
= 87.92 inches.
2. Convert the circumference of the wheel to feet:
Circumference in feet = 87.92 inches * (1 foot / 12 inches)
= 7.3267 feet.
3. Calculate the RPM:
RPM = 475,200 feet per hour / 7.3267 feet
≈ 64,870.31 revolutions per minute.
Therefore, the spin balancer should be set to approximately 64,870 RPM to balance the tires at a speed of 90 miles per hour when the wheel has a radius of 14 inches.
To determine the revolutions per minute (RPM) required for a spin balancer to balance the tires at a given speed, you need to consider the circumference of the wheel, as well as the speed of the car.
First, let's convert the speed from miles per hour to inches per minute, as RPM is generally measured in minutes.
For a wheel with a radius of 16 inches:
1. Calculate the circumference of the wheel using the formula: circumference = 2 * π * radius.
- Plugging in the value, we get: circumference = 2 * 3.14159 * 16 = 100.53096 inches.
2. Convert speed from miles per hour to inches per minute:
- There are 5,280 feet in a mile, and 12 inches in a foot, so 1 mile = 5,280 * 12 = 63,360 inches.
- Divide the speed (90 miles per hour) by the conversion factor of inches per mile to get inches per hour:
- 90 * 63,360 = 5,702,400 inches per hour.
- Divide the result by 60 (minutes) to find inches per minute:
- 5,702,400 / 60 = 95,040 inches per minute.
3. Calculate the RPM by dividing the speed in inches per minute by the circumference of the wheel:
- RPM = inches per minute / circumference
- RPM = 95,040 / 100.53096
- RPM ≈ 946.48
Therefore, a spin balancer should be set to approximately 946.48 RPM to balance the tires at a speed of 90 miles per hour for a wheel with a radius of 16 inches.
For a wheel with a radius of 14 inches, you can follow the same steps:
1. Calculate the circumference of the wheel:
- circumference = 2 * π * radius = 2 * 3.14159 * 14 = 87.9646 inches.
2. The speed in inches per minute remains the same, as it is a constant:
- inches per minute = 95,040 inches per minute.
3. Calculate the RPM:
- RPM = inches per minute / circumference
- RPM = 95,040 / 87.9646
- RPM ≈ 1,080.91
Therefore, for a wheel with a radius of 14 inches, the spin balancer should be set to approximately 1,080.91 RPM.