# I Types of Acceleration

1. Apr 27, 2018

### physea

Hello,

I am confused about the types of acceleration in rotational movement of rigid bodies.

I am quite clear about the various types of movement of rigid bodies. The body can have translational movement where acceleration is dV/dt. But what are the other types of acceleration that the body may have?

I think we can categorise the other types of movements into rotational through the centre of mass and rotational through a centre outside the centre of mass.

Can you tell me please the equations that describe these? It is not clear and I see confusing things on the web, for example that a=ra.

Thanks!

2. Apr 27, 2018

### jbriggs444

Any rigid motion can be characterized as a translation plus a rotation. You can choose any point you like to describe the rotation. Depending on the point you choose, the corresponding translation may be different.

For instance, a rolling wheel can be described as a translation of the axle and a rotation about the axle. Or it can be described (momentarily at least) as a rotation about the instantaneous point of contact with the road.

3. Apr 27, 2018

### osilmag

a=ra is the equation for rotational acceleration. It is usually written as a=r*alpha

4. May 2, 2018

### physea

Can anyone explain what is a and what alpha?

5. May 3, 2018

### olgerm

acceleration in circular movement is $a=\omega^2\cdot r$
• a is acceleration.
• $\omega$ is angular velocity.
• r is radius of trajectory.

6. May 4, 2018

### physea

Ok, but you say it's omega squared, while @osilmag said it's simply omega!

7. May 4, 2018

### sophiecentaur

Omega squared is the correct one.

8. May 4, 2018

### physea

Are you sure?
It's x = rθ
So derivative of x = r times derivative of θ
So second derivative of x = r times second derivative of θ which is linear acceleration = r times angular acceleration

How can angular velocity (ω) be the square of angular acceleration?

9. May 4, 2018

### sophiecentaur

If there is a misunderstanding here, then why not just look it up? Afaiac acceleration under circular motion is ω2r. Can you find a source that says otherwise.
This stuff is not really a matter of discussion. It's all written down and the definitions are accepted.

10. May 4, 2018

### physea

I don't want to just look it up, if I wanted to do that I would do it and wouldn't come here, but I suppose this is not the intention always as this forum would have no meaning.

I want to know how these are derived and related together.

So, I know that x=rθ.
From that, don't we derive that V=rω and γ=rα ? Aren't these correct so far?

How can α=rω^2 ?

By the way:
α = angular acceleration
γ = linear acceleration

11. May 4, 2018

### A.T.

Where did you get that from?

12. May 4, 2018

### physea

13. May 4, 2018

### A.T.

14. May 4, 2018

### physea

Yeah, α = angular acceleration. I wrote the same.
α=rω^2

15. May 4, 2018

### A.T.

If you think you wrote the same as olgerm, then you need to use a bigger font, or better glasses.

16. May 4, 2018

### physea

OK so you mean that γ=rω^2 then.
And we know that γ=rα
So α=ω^2. Is this true? The angular acceleration is the square of the angular velocity?

17. May 4, 2018

### A.T.

Where did you get that from?

18. May 4, 2018

### physea

We know that x=rθ
Then x'=rθ'
So x''=rθ'' which is γ=rα.

19. May 4, 2018

### sophiecentaur

@physea What source are you using for your opinions and statements? I have a feeling that you are trying to self-drive through this topic and that you are trying to use Q and A to learn the stuff. This is not a good way (as you are demonstrating with many of your posts). You seem to be mixing up ideas and symbols, which may be why you arrive at things like "α=ω^2.", which is a nonsense statement where an acceleration is equated to a velocity squared. You would, I'm sure, never do that for linear motion.
You need a half decent mechanics book.

20. May 4, 2018