# Terminology in rotational kinematics: distance vs displacement

1. Apr 18, 2013

### JeanJean

I'm trying to learn some physics on my own, using the internet as my main source of information.
Now, I'm a bit confused about some terminology, and I can't find anything about it...

Distance vs displacement in rotational kinematics!

Is there a similar difference as in linear kinematics?

If a wheel turns 2.5 revolutions, would it be:
distance = 2.5 rev
displacement = 0.5 rev

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 18, 2013

### voko

Your understanding is correct. Even if one rarely uses the idea of "distance" in rotational kinematics, and the "displacement" is usually simply "the angle".

3. Apr 18, 2013

### ap123

Isn't the angular displacement = 2.5 rev ?

4. Apr 18, 2013

### voko

Any displacement is the difference between some start and some end position. Even though there can be a kazillion revolutions done in between.

5. Apr 18, 2013

### ap123

My understanding is that the angular position at the end will reflect the number of revolutions.

If, for example, you use the equations for constant angular accceleration, the angular displacement can easily be more than 1 revolution.

6. Apr 18, 2013

### voko

This is complicated by the ambiguity in the angular position. Add $2 \pi$ to any position, it is still the same position.

The difference between angular distance and angular displacement is most obvious when the body under consideration never makes a complete revolution but goes back in forth.

7. Apr 18, 2013

### ap123

This would appear to be clear, but if you're using the equations for constant angular acceleration you have a problem.
For example, let
Δθ = (1.0 rev/s)t
For any t>1s, the angular displacement must be >1.0rev

8. Apr 18, 2013

### JeanJean

I see it is all a matter of interpretation and/or definition...

But... isn't there some 'official definition' ?
How is this taught in school ?