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Oscillation (particle movement)

  1. Apr 15, 2014 #1
    1. The problem statement, all variables and given/known data
    A particle rotates counterclockwise in a circle
    of radius 4.4 m with a constant angular speed
    of 11 rad/s. At t = 0, the particle has an x
    coordinate of 2.9 m and y > 0 .
    Part 1: Determine the x coordinate of the particle velocity
    at t = 1.22 s.
    Answer in units of m/s

    Part 2: Determine the x coordinate of the particle acceleration
    at t = 1.22 s.
    Answer in units of m/s2


    2. Relevant equations
    x = Acos(wt + d)
    where d was found in a previous part of the problem and confirmed correct by the program to be:
    d = 0.8511870029
    v = -wAsin(wt + d); vx = -wRsin(wt) = -vsin(wt)
    a = -w2Acos(wt + d)

    Note R and A are interchangeable

    3. The attempt at a solution
    Part 1:
    Attempt 1: v = -wAsin(wt + d) = -(4.4 m)sin(11rad/s * 1.22s + 0.8511870029)
    v = -4.360544081 m/s
    Incorrect
    Attempt 2: vx = -wRsin(wt)
    vx = -(11rad/s)(4.4m)sin(11 rad/s * 1.22 s) ≈ -36.477666 m/s
    vx = -vsin(wt) = (solution from Attempt 1)sin(wt)
    vx = -(-4.360544081 m/s)sin(11 rad/s * 1.22 s) ≈ -3.286414681 m/s

    Vastly different answers, don't know if incorrect because I don't want to get points deducted from score from trying random answers
     
  2. jcsd
  3. Apr 15, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Attempt 1: v = -wAsin(wt + d) = -(4.4 m)sin(11rad/s * 1.22s + 0.8511870029) is almost correct. You put A=4.4m into -wA. What happened to the w?
     
  4. Apr 15, 2014 #3
    that's true. So if I multiply my result by 11 rad/s I get:
    v = -47.96598498 m/s

    However, is this total velocity in both x and y directions or is it the x coordinate of the velocity?

    I would think that it would be the x coordinate, since we are taking the derivative of the position of the x coordinate?
     
  5. Apr 15, 2014 #4
    Ok part 1 is correct!
     
  6. Apr 15, 2014 #5
    Part 2: Determine the x coordinate of the particle acceleration
    at t = 1.22 s.
    Answer in units of m/s2


    a = -w2Acos(wt + d)
    a = -(11 rad/s)2(4.4 m)cos((11 rad/s * 1.22 s) + 0.8511870029)
    a = 71.13887508 m/s2

    which is correct!

    Thank you.

    But now I have more of a conceptual question that I would like to ask? Or rather, methodological?

    I have a test coming up in 2 days over Dynamics of a Rigid Body, Statics and Elasticity, Oscillations, and Waves. (All in my Mechanics class)

    Since it is my freshman year, taking mechanics, as a Physics major, I was wondering how it is that others study physics, or if you both could give me words or advice on how I should approach the study of physics.

    Up until this point, I would read the textbook, work problems relevant to the readings, and if I was still confused I would Google the problem or concept.
    I am not dissatisfied with this method, but I was just looking for someone else's perspective.
     
  7. Apr 15, 2014 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Very welcome! What you are doing sounds fine to me, it worked for me. Except I didn't have google. But if you want more opinions on this there is a separate forum called Academic Guidance. You might want to post there. You'll probably get too many opinions, but there you go.
     
    Last edited: Apr 15, 2014
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