If a flywheel is 4 feet in diameter. Find the speed of a belt which drives the wheel at 400 revolutions per minute?
One rotation is 4π feet of belt.
so the belt moves at 400(4π) ft/min
= 1600π ft/min
To find the speed of the belt, we need to first determine the circumference of the flywheel.
The circumference of a circle can be calculated using the formula:
Circumference = π * Diameter
Given that the diameter of the flywheel is 4 feet, the circumference can be calculated as follows:
Circumference = π * 4 = 4π feet.
Next, we need to calculate the distance traveled by the belt in one minute, which is equal to the circumference of the flywheel times the number of revolutions per minute.
Distance = Circumference * Revolutions per Minute
In this case, the distance is:
Distance = 4π * 400 = 1600π feet.
Finally, the speed of the belt is equal to the distance traveled in one minute. Therefore, the speed of the belt is:
Speed = 1600π feet per minute.
This is the answer in terms of π, an irrational number. However, if you prefer a numerical value, you can approximate π as 3.14 and calculate the speed accordingly:
Speed ≈ 1600 * 3.14 ≈ 5024 feet per minute.