Question

You are given that a wheel has a radius of 2 feet and a spin rate of 10 revolutions per minute. Describe how you would determine the linear velocity, in feet per minute, of a point on the edge of the wheel. State the linear velocity of the wheel, and explain why your answer is reasonable.

Answer 1

Sample Response: I am asked to find linear velocity and am given revolutions per minute. Since there are 2pi radians in 1 revolution, I can convert rpm to radians per minute by multiplying by 2pi. The angular displacement is 20pi radians, so the angular velocity is 20pi radians per minute. Next, I know that linear velocity is equal to angular velocity times the radius. Using 3.14 for pi and multiplying 20pi by 2 feet, I approximate the linear velocity as 125.6 feet per minute. This linear velocity of 125.6 divided by the radius of 2 feet does give me 62.8 radians per minute. Since 62.8 radians per minute is about 20pi radians per minute, this checks. Linear velocity is arc length over time. I can see if this result is reasonable by finding the arc length. The circumference of the wheel is 4pi or about 12.5 feet. If a point on the edge of the wheel can travel about 12.5 feet in 1 revolution, then it travels about 125 feet in 10 revolutions. It is reasonable for the linear velocity to be about 125.6 feet per minute.

Explanation:

Answer 2

About 126 ft/min

Explanation:

We know r = 2 feet, and that the wheel has an angular speed of 10 rpms, or 10 revolutions per minute. Our goal is to get the speed in ft/sec.

10 rev 1 minute 2π radians 2 feet

----------- × ---------------- × ------------------ × ------------

1 minute 60 seconds 1 revolution 1 radian

= 10 * 2π * 2 = 126 ft/minute

The answer is reasonable. Another, simple approach to this would be using the formula 2π * r * rpm. If so, 2π * 2 * 10 which would be 126 ft/minute.