A wheel with a 22 inch diameter is turning at the rate of 31 revolutions per minute. What is the linear speed of a point on the rim, measured to the nearest inch per minute?
speed= 22in*2PI*31 in/sec
To find the linear speed of a point on the rim of the wheel, we can use the formula:
Linear Speed (V) = Circumference × Number of revolutions per minute
First, let's calculate the circumference of the wheel using the diameter. The formula for the circumference (C) of a wheel is given by:
C = π × Diameter
Given that the diameter of the wheel is 22 inches, we can substitute the value into the formula:
C = π × 22 inches
Now, let's calculate the number of inches the wheel travels in one revolution:
Inches per Revolution = Circumference
Next, we can find the linear speed by multiplying the inches per revolution by the number of revolutions per minute:
Linear Speed = Inches per Revolution × Number of revolutions per minute
Substituting the values we know:
Linear Speed = (π × 22 inches) × 31 revolutions per minute
Using the approximation value of π as 3.14, we can calculate:
Linear Speed ≈ (3.14 × 22 inches) × 31 revolutions per minute
Simplifying the equation:
Linear Speed ≈ 68.876 inches per minute
Therefore, the linear speed of a point on the rim of the wheel is approximately 68.876 inches per minute, rounded to the nearest inch per minute.