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Conceptual question about angular speed and radius for rotational motion

  1. Apr 8, 2008 #1
    let's say a wheel rotates with a constant angular acceleration. Would its angular speed be affected if the radius was changed? It seems that angular speed would be independent of the radius since the angle is just a proportional quantity.
     
  2. jcsd
  3. Apr 8, 2008 #2

    dst

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    It depends on your assumptions. For a constant angular momentum, the angular frequency decreases with a larger radius - the moment of... something I can't remember at 5:00AM... gets larger since it's proportional to distance from axis - just like a lever.

    On the other hand, for a constant angular acceleration, angular acceleration remains... constant.

    Edit: Torque. It has the same units as a moment of whatever I can't remember.
     
    Last edited: Apr 9, 2008
  4. Apr 9, 2008 #3
    so angular speed is dependent on radius since the force that moves the wheel would cause a greater acceleration if the wheel had a smaller radius (meaning it would be a smaller wheel)? also assuming the force that moves the wheel stays constant.
     
  5. Apr 9, 2008 #4

    dst

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    Exactly so. Try it yourself, spin around first like a ballerina with your arms extended then like a spinning... cylinder and observe. You will look like a muppet on both accounts but it's all in the name of physics.
     
  6. Apr 10, 2008 #5
    Thanks.

    Btw, i will only look like a muppet if someone is looking.
     
  7. Apr 10, 2008 #6

    rbj

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    Torque, measured in units of force times length has the same dimension as work or energy. and that is legitimate; turning a shaft exactly one radian of twist (and the radian is the mathematically natural unit of twist) the number of newton-meters of torque becomes exactly the number of Joules of work done. so with a twist of one radian, torque is the same as energy.
     
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