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: Point on Spinning Circle

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data

    See image.

    2. Relevant equations
    ωx (ωx r) = anormal
    αx r =atangent


    3. The attempt at a solution

    I solved for w=2 k rad/s and α= -1.5 k rad/s

    I also got the correct answer using the cross products. My problem is I am trying to do this problem in rectangular coordinates (I really like rectangular), but I am doing something wrong and I cannot see it.

    So, I assume r is constant:
    x''=-r*cos(45)[ω^2-α] = Correct answer= -15.566

    BUT, y'' is giving me a headache:
    I keep getting rsin(45)[ω^2-α] and I get = 15.66 and NOT the right answer of 7.07 in/s. There is a lurking negative sign and I cannot find it. That - should be a + and then I get a correct answer. Am I just deriving incorrectly?

    And apologizes if this is pretty novice: its from my Junior-level engineering class...or a freshman Physics class. ;p

    Attached Files:

    • rage.png
      File size:
      41.5 KB
    Last edited: Sep 20, 2012
  2. jcsd
  3. Sep 20, 2012 #2


    Staff: Mentor

    from the problem you know that va = 8 in/sec and aa=6 in/sec/sec

    and you know that va is tangent to the circle and that aa is along the radius

    so the unit vector for aa=cos (theta) i + sin(theta) j

    and the unit vector for va = - sin(theta) i + cos(theta) j

    now figure out theta and factor in the vector magnitudes into the unit vector equations to get the vector equations of motion.

    Lastly, if you do unit vector va dot aa = -sin(theta) cos(theta) + cos(theta) sin(theta) = 0 meaning they are perpendicular as a check
  4. Sep 21, 2012 #3
    That make's sense. Shouldn't I be able to use y=-rsin*theta to kind of derive that? Everything you said makes perfect sense (I do like the dotting notion!), but I am still wondering why rectangular equation has issues.
  5. Sep 21, 2012 #4


    Staff: Mentor

    you should be able to start with s(x,y) and then diferentiate to get va
    and differentiate again to aa.

    s(x,y) = R*cos(w*t + offset)) i + R*sin(w*t + offset) j

    make sure you're using radian measure for all angle values that could be where your problem lies.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook