# Homework Help: Angular and linear velocity

1. Dec 12, 2012

### Bananas40

First of all, I very much thank you for reading this. I was asked the following:
'The wheels of a tractor have different radius. Is their angular velocity equal or different? And the linear velocity?'

I thought that, due to the fact that the smaller wheels take less time to spin 2π rad tan the big ones, their angular velocity will be bigger. I'm not really sure about the linear velocity.

2. Dec 12, 2012

### TSny

Hello, and welcome to PF!

The "linear velocity" of a wheel is the linear velocity (with respect to the ground) of the point at the center of the wheel. Does that help with comparing the linear velocities of the bigger and smaller wheels?

3. Dec 12, 2012

### Bananas40

So is it the same as the angular velocity? And what about the angular velocity? Is what I said true?
In fact, I'm asking this because this question appeared in an exam I've taken today. According to my teacher, the angular velocity is the same for both wheels, but I (as well as a couple of my classmates) think he isn't right.

4. Dec 12, 2012

### TSny

Not sure how you're using "it". Linear velocity is of course not the same thing as angular velocity.

When the tractor is moving along, the center of each wheel must move with the same speed as the tractor. The center is connected to the axle which is connected to the tractor. So, the center of the big wheel and the small wheel move at the same linear speed as the tractor.
Yes, you are correct about angular velocity. The best way to see why is to first see that the linear velocity must be the same and then to consider how linear velocity is related to angular velocity for a rolling wheel.
I'm with you.

5. Dec 12, 2012

### Bananas40

You're right. Sorry for my poor English.

Actually, that's exactly what I wrote in the exam: The wheels have different angular velocity and the same linear velocity. However, we asked our teacher after the exam and he replied with the complete opposite. I really hope I'll be able to convince him, because that question carried 20% of the exam mark.

6. Dec 12, 2012

### haruspex

Ask your teacher how long it will take for the rear wheels to overtake the front ones.

7. Dec 12, 2012