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.

Answer 1

126.71 feet per minute

You can use any one of the following reasonable explanations:

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:

the next question has the explanation. So you can write in your own words.

Multiply revolutions per minute by 2pi to get the angular velocity in radians per minute.

Approximate the linear velocity by multiplying the angular velocity by the radius.

Check the calculation by dividing the linear velocity by the radius to get the angular velocity.

Determine the reasonableness of the answer by finding the arc length for 10 revolutions.

Answer 2

Linear velocity of point on the edge of wheel having radius of 2 feet and spin rate of 10 revolution per minute is 125.71 feet per minute.

Explanation:

Given that radius of wheel = 2 feet

There is a point on edge of the wheel .we need to determine linear velocity of that point.

Let’s first calculate distance covered by a point when 1 revolution of wheel is complete.

When one revolution is complete the distance traveled by a point on edge of the wheel will be equal to circumference of the wheel

In one revolution, point covers distance of feet

So in 10 revolution, point covers distance of

Given that in a minute, wheel takes 10 revolution.

Which means in a minute , point covers feet that is feet per minute = 125.71 feet per minute

Hence linear velocity of point on the edge of wheel having radius of 2 feet and spin rate of 10 revolution per minute is 125.71 feet per minute.