1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Methods for calculating average velocity

  1. Feb 15, 2015 #1
    1. The problem statement, all variables and given/known data
    A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to θ(t)=γt+βt3, where γ= 0.383 rad/s and β= 1.00×10−2rad/s3.

    Calculate the average angular velocity ωav−z for the time interval t=0 to t= 5.50s.

    2. Relevant equations

    3. The attempt at a solution
    Okay so I solved all the questions above this one which gave me the final and initial angular velocities and I got ωi = 0.383 rad/s and ωf = 1.29 rad/s.

    When I calculate average angular velocity, why can't I use (ωi + ωf)/2
    Instead, I have to use (Θf - Θi)/5.50 to get the correct answer. Shouldn't the first equation yield the same result because an average is the sum of the velocities divided by 2?
  2. jcsd
  3. Feb 15, 2015 #2


    User Avatar
    Homework Helper

    Nooo this is not true at all!

    This only applies to one very special case: constant acceleration.

    The average speed (over an interval of time) is the constant speed which produces the same displacement (over the same interval). So if you imagine a graph like y(x) or v(t) then the average is the constant (a horizontal line) which produces the same area (over a certain interval of x or t) as the area under the actual curve.

    In the special case where y(x) or v(t) has a constant slope (a.k.a. constant acceleration) the average happens to be the midpoint of the line and thus is (y(a)+y(b))/2
    (You might like to convince yourself that the midpoint between to points on a graph with a constant slope is the only constant value which gives the same area between the two points.)

    I hope I'm not making it confusing, but words tend to do that with visual ideas. It is important to remember that the (y(a)+y(b))/2 or (vi+vf)/2 is just a special case which only applies for constant slope (constant acceleration).
  4. Feb 15, 2015 #3
    If the angular acceleration is constant, can (vi+vf)/2 be used?
  5. Feb 15, 2015 #4


    User Avatar
    Homework Helper

    Yes. If and ONLY if the angular acceleration is constant.
  6. Feb 15, 2015 #5
    What do you think is the more general case of avg velocity?

    Think: if I went 100 miles in 2 hours, my avg was?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted