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Rotational Dynamics of a disk

  1. Jul 30, 2006 #1
    Hello,
    I was able to solve this problem fine, but I had a question about it:

    "A disk 8.00 cm in radius rotates at a constant rate of 1200 rev/min about its central axis. Determine (a) its angular speed, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on a rim, and (d) the total distance a point on the rim moves in 2.00 s."

    In solving the problem, I first converted the given information to SI units.
    In solving for (a), the angular speed is given. It's only the conversion that was necessary, so a = 125.6 rad/s. In solving for b, I realized that tangential speed (v) = rw (where w is the greek letter omega, representing angular velocity). Multiplying the r and w gives you 3.79 m/s. Part C is where my question lies: I understand that radial/centripetal acceleration = v^2/r which = rw^2. If I plug in the given values for v^2/r (3.79^2/0.08), I don't get the right answer. If I plug in the values for rw^2, I do. If they're equivalent to each other, how come the answers aren't matching up?

    Thank you.
     
  2. jcsd
  3. Jul 30, 2006 #2

    Chi Meson

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    radial acceleration is not the same as centripetal acceleration.

    Radial acceleration (alpha) is the rate at which angular velocity changes, which is "delta omega" over t. Since the angular velocity is constant, you don't need a calculator to get radial acceleration.

    Your two answers for the centripetal acceleration are different because you are using the tangential speed for a point at 3 cm, not a point on the rim at 8 cm. Neither gives you the correct answer for radial acceleration though.

    Centripetal acceleration is the rate at which a particle's velocity changes in direction (as opposed to the rate of changing magnitude of velocity--that's tangential acceleration).
     
    Last edited: Jul 30, 2006
  4. Jul 30, 2006 #3
    My professor has said that radial and centipetal acceleration/force are the same thing. Or is it just force that is equivalent? You said radial acceleration is alpha, but alpha is used throughout the chapter as angular accleration. Is angular and radial acceleration the same thing then?

    Thanks for your reply.
     
  5. Jul 30, 2006 #4

    Chi Meson

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    Oh my god my brain is fried. For some reason I confused the word "radial" with "angular." Your professor is correct, I was...it's hot here OK?

    I think I'm correct in answering your actual question, right?
     
  6. Jul 30, 2006 #5
    Haha, okay. Thanks for clearing that up.

    Yes, in answering my direct question, what you said makes perfect sense.
     
  7. Aug 2, 2006 #6
    I would use different terms; normal acceleration, for acceleration of the rim towards to axis, angular acceleration for the rotational acceleration sould omega change with time. That way you don't get confused.
     
  8. Aug 4, 2006 #7

    Chi Meson

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    the word "normal" already has a specific meaning when regarding circles; it refers to the direction that perpendicular to the plane of the circle. In other words, the direction parallel to the axis.
     
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