A wheel with a 24-inch diameter is turning at the rate of 32 revolutions per minute. To the nearest inch per minute, what is the linear velocity of a point on the rim?
one circumference = 2π(12) = 24π inches
in one minute it covers 32(24π) or 768π inches
so the linear velocity is 768π inches/min
= appr 2413 inches/min
12*32*2pi = 2413
cool.
thank you
To find the linear velocity of a point on the rim of the wheel, we can use the formula:
Linear velocity = (circumference of the wheel) × (number of revolutions per minute)
First, let's find the circumference of the wheel. The formula for the circumference of a circle is:
Circumference = π × diameter
Given that the diameter of the wheel is 24 inches, we can substitute this value into the formula to find the circumference:
Circumference = π × 24 inches
Now, let's calculate the circumference:
Circumference = 3.14 × 24 inches
Circumference ≈ 75.36 inches
Next, we can substitute the circumference and the given rate of 32 revolutions per minute into the linear velocity formula:
Linear velocity = 75.36 inches × 32 revolutions per minute
Calculating the linear velocity:
Linear velocity ≈ 2411.52 inches per minute
Rounding this value to the nearest inch gives us the final answer:
Linear velocity ≈ 2412 inches per minute
Therefore, the linear velocity of a point on the rim of the wheel is approximately 2412 inches per minute (to the nearest inch per minute).
To find the linear velocity of a point on the rim of a wheel, we need to calculate the distance traveled by that point in one minute.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 24 inches, so the circumference is:
C = π * 24 inches
Next, we need to calculate the distance traveled by the point on the rim of the wheel in one revolution. Since the circumference represents one complete revolution, the distance traveled in one revolution is equal to the circumference.
Therefore, the distance traveled in one revolution is:
distance = π * 24 inches
Since the wheel is turning at the rate of 32 revolutions per minute, we can multiply the distance traveled in one revolution by 32 to get the total distance traveled in one minute:
total distance = 32 * π * 24 inches
Now we have the total distance traveled in one minute, but we need to find the linear velocity, which represents the rate of change of the distance in one minute. Thus, the linear velocity would be:
linear velocity = total distance / time
In this case, the time is one minute, so we can substitute total distance with 32 * π * 24 inches:
linear velocity = (32 * π * 24 inches) / 1 minute
Finally, we can calculate the linear velocity by evaluating this expression. Rounding the answer to the nearest inch per minute will give us the final result.