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: Angular Motion

  1. May 28, 2010 #1
    1. The problem statement, all variables and given/known data

    A uniform rod of length 0.750 m and mass 1.20 kg is pivoted at one end by a smooth pin as shown below. The rod is released from the vertical position and given a slight nudge to release it from the vertical position of unstable equilibrium.

    [PLAIN]http://img175.imageshack.us/img175/9820/angacc40pc.png [Broken]

    When the rod is horizontal:

    (a) Calculate its angular acceleration.

    (b) Calculate the x and the y components of the acceleration of the centre of mass.

    3. The attempt at a solution

    First I focus on part (a). I have already obtained the angular velocity:

    The potential energy of the system relative to the reference configuration is MgL/2 because the center of mass of the rod is at a height L/2 away from its position in the reference configuration. Conservation of mechanical energy for the system is:

    Ki+Ui = Kf + Uf


    [tex]\omega = \sqrt{\frac{MgL}{\frac{1}{3}ML^2}} = \sqrt{\frac{3g}{L}}[/tex]

    using the given values I get ω=6.26 rad/s, which is the correct velocity.

    Now I want to use the equation [tex]\alpha = \frac{\Delta \omega}{t}[/tex] to find the angular acceleration. Here's where I'm stuck. Could anyone please show me how to find the time for this equation?

    Correct answer to part (a) is 19.62 rad/s² and for part (b) it is -14.7 m/s²(x-component) and -7.36 m/s² (y-component)
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 28, 2010 #2


    User Avatar
    Homework Helper

    No, you can not use

    \alpha = \frac{\Delta \omega}{t}
    as it is valid for uniform acceleration only, and you do not know if the acceleration is uniform; neither you know the time.

    There is a formula betwee torque, angular acceleration, and moment of inertia. Use that.

  4. May 29, 2010 #3
    Thank you very much, I got it. Now could you explain how to deal with part (b)? How do we calculate the x (or y) component of the acceleration of the centre of mass? I'm not quite sure what that even means since I don't have any worked examples in my textbook.
  5. May 29, 2010 #4


    User Avatar
    Homework Helper

    The centre of mass moves along a circle, and the angular velocity is not constant. What components of acceleration has a body performing circular motion?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook