A pulley, 26 inches in diameter, is driven at 360 rpm by a belt. How fast is the belt moving?
360 rev/min * 26π in/rev = 9360π in/min
To find the speed of the belt, we can use the formula:
Speed = (π x diameter x RPM) / 12
Given:
Diameter = 26 inches
RPM = 360
Let's substitute the values into the formula:
Speed = (π x 26 x 360) / 12
= (3.14 x 26 x 360) / 12
= (81,878.4) / 12
= 6,822.36 inches/minute
Therefore, the speed of the belt is approximately 6,822.36 inches per minute.
To find the speed of the belt, we need to calculate the circumference of the pulley and then multiply it by the rotational speed (rpm) of the pulley.
The formula to calculate the circumference (C) of a circle is:
C = π * diameter
Given that the diameter of the pulley is 26 inches, we can calculate the circumference:
C = π * 26 inches
Next, we need to convert the rotational speed (rpm) of the pulley to inches per minute. To do this, we can use the conversion factor of 1 revolution = 2πr, where r is the radius of the circle.
The formula to convert rpm to inches per minute is:
Inches per minute = rpm * circumference
First, we need to convert rpm to revolutions per minute:
Revolutions per minute = rpm
Now, we can calculate the inches per minute:
Inches per minute = Revolutions per minute * circumference
Let's calculate it step by step:
C = π * 26 inches
C ≈ 3.14159 * 26 inches
C ≈ 81.68141 inches (approximately)
Inches per minute = 360 rpm * 81.68141 inches
Inches per minute ≈ 29445.3076 inches per minute (approximately)
Therefore, the belt is moving at approximately 29445.3076 inches per minute.