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Average angular speed

  1. Mar 21, 2007 #1
    1. The problem statement, all variables and given/known data
    A grindstone of radius 4.0m is initialy spinning with an angular speed of 8.0 rad/s. The angular speed is the increased to 10rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. What is the average angular speed of the grindstone?

    2. Relevant equations
    Please check work.....

    3. The attempt at a solution

    avg w= (delta theta)/delta T
    = (10 rad/s - 8 rad/s) / (4 s-0)
    = .5 rad/s

    Vt= r * avg w
    = 4m * .5 rad/s
    = 2 rad/s
  2. jcsd
  3. Mar 21, 2007 #2

    Doc Al

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    Staff: Mentor

    What you calculated is the average angular acceleration, not the average angular speed. (Even though your equation was correct--change in theta over time--what you put into the equation was change in angular speed over time. You might have caught the error if you checked your units.)

    Sanity check: If it starts at 8 rad/s and speeds up to 10 rad/s--how can the average speed be only 2 rad/s??? :wink:
    Last edited: Mar 21, 2007
  4. Mar 21, 2007 #3
    This is where I get confused with Physics. Are speed and velocity the same thing?

    Redoing the math, which I hope is right:

    Avg speed is (10 rad/s + 8 rad/s) / 4 s = 4.5 rad/s

    Vt = r*w = 4 m * 4.5 rad/s = 18 rad/s

    Or do I not need to go as far to find Vt?
  5. Mar 21, 2007 #4
    Velocity is a vector while speed is a scalar quantity. Always keep that in mind.
  6. Mar 21, 2007 #5
    I think I found it in the text book:

    Since the angular acceleration is constant:
    Avg ang velocity= 1/2[wo + w] = 1/2[8+10]= 9 rad/s
  7. Mar 21, 2007 #6


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    Gold Member

    I assume the question is asking for the average angulat speed during the 4s of acceleration. To get this, you need to calculate how far it turns ( in radians) and divide by 4s.

    Remember this

    distance = 1/2 * acceleration * time^2

    for linear motion.

    So for angular motion

    angle turned = 1/2 * ang. acc. * time^2

    Do you follow ?
  8. Mar 21, 2007 #7

    Doc Al

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    Staff: Mentor

    Again, this equation fails the "common sense" test. You start out at 8 rad/s and end up at 10 rad/s--so don't you think the average speed must be somewhere in the middle of those two speeds?

    And the units don't match--you divide by time, but still your answer is in rad/s. (Dividing rad/s by s gives you units of rad/s^2--which are the wrong units for angular speed.)

    Now you've got it. :smile:
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