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I Types of Acceleration

  1. Apr 27, 2018 #1
    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. jcsd
  3. Apr 27, 2018 #2

    jbriggs444

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    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.
     
  4. Apr 27, 2018 #3
    a=ra is the equation for rotational acceleration. It is usually written as a=r*alpha
     
  5. May 2, 2018 #4
    Can anyone explain what is a and what alpha?
     
  6. May 3, 2018 #5
    acceleration in circular movement is ##a=\omega^2\cdot r##
    • a is acceleration.
    • ##\omega## is angular velocity.
    • r is radius of trajectory.
     
  7. May 4, 2018 #6
    Ok, but you say it's omega squared, while @osilmag said it's simply omega!
     
  8. May 4, 2018 #7

    sophiecentaur

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    Omega squared is the correct one.
     
  9. May 4, 2018 #8
    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?
     
  10. May 4, 2018 #9

    sophiecentaur

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    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.
     
  11. May 4, 2018 #10
    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
     
  12. May 4, 2018 #11

    A.T.

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    Where did you get that from?
     
  13. May 4, 2018 #12
     
  14. May 4, 2018 #13

    A.T.

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  15. May 4, 2018 #14
    Yeah, α = angular acceleration. I wrote the same.
    α=rω^2
     
  16. May 4, 2018 #15

    A.T.

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    If you think you wrote the same as olgerm, then you need to use a bigger font, or better glasses.
     
  17. May 4, 2018 #16
    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?
     
  18. May 4, 2018 #17

    A.T.

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    Where did you get that from?
     
  19. May 4, 2018 #18
    We know that x=rθ
    Then x'=rθ'
    So x''=rθ'' which is γ=rα.
     
  20. May 4, 2018 #19

    sophiecentaur

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    @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.
     
  21. May 4, 2018 #20

    A.T.

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