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