1. Not finding help here? Sign up for a free 30min 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!

Non-uniform circular motion

  1. Oct 2, 2008 #1
    1. The problem statement, all variables and given/known data
    An object of mass m is constrained to move in a circle of radius r. Its tangential acceleration as a function of time is given by [tex]a_{tan} = b + ct^2[/tex], where b and c are constants.

    A) If [tex]v = v_0[/tex] at t = 0, determine the tangential component of the force, [tex]F_{\tan }[/tex], acting on the object at any time t > 0.
    Express your answer in terms of the variables m, r, [tex]v_0[/tex], b, and c.

    B) Determine the radial component of the force [tex]F_{\rm{R}}[/tex].
    Express your answer in terms of the variables m, r, [tex]v_0[/tex], b, t, and c.

    2. Relevant equations
    [tex]a_{tan} = b + ct^2[/tex]
    Newton's Laws

    3. The attempt at a solution
    A. was not a problem for me:

    For B.:
    It seems to make sense that because v is tangential speed we could use...
    So that...
    Finally giving...

    Which is not correct. What did I do wrong?
  2. jcsd
  3. Oct 3, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Symstar! Welcome to PF! :smile:
    That only works if atan is constant, doesn't it? :wink:

    Hint: dv/dt = … ? :smile:
  4. Oct 3, 2008 #3
    Re: Welcome to PF!

    dv/dt = atan correct?

    So would I need to integrate?
    [tex]\int a_{tan} = \int b + ct^2[/tex]
    [tex]\frac{dv}{dt}= bt+\tfrac{1}{3}ct^3[/tex]

    And it seems logical in our case that +C would actually be +v0

    Which would end up giving me:

    Which I just confirmed to be the correct answer... thanks for you your help tim.
    Last edited: Oct 3, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Non-uniform circular motion