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: 2D Rigid Body Dynamics - Newtonian Equaitons of Motion

  1. Jan 8, 2014 #1
    1. The problem statement, all variables and given/known data
    In the diagram attached a bar weighs 500 kg and is a 2D plane rigid body with mass centre at G. At the instant shown, the bar is moving horizontally at but reducing speed, causing horizontal deceleration as shown by vector a=-7i m/s2. At the same time, the bar is being raised rapidly by anti-clockwise rotation of the support structure with angular velocity of magnitude ωr=2rad/s. All other kinematic components can be ignored. Assuming the forces at B can only be applied in the normal direction and that the support at point O is a frictionless pin joint construct Newtonian equations of motion, and use just the moment equation about Point O to calculate the instantaneous force in the hydraulic ram at point B.

    2. Relevant equations
    ∑Fx = m*ax

    ∑Fy = m*ay

    ∑Mo = I*[itex]\alpha[/itex]+m*ad

    3. The attempt at a solution

    I can see using the equations below that I[itex]\alpha[/itex]=0 as there is no angular acceleration. I am struggling to work out what the acceleration component is in the "m*a*d" part of the equation. Can anyone please have a go at explaining (not solving) how I can find it?



    Attached Files:

  2. jcsd
  3. Jan 8, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    The rod is rotating anticlockwise, at a constant angular speed, about one end as that end moves to the right and decelerates.

    Presumably there is an unbalanced centripetal force on the rod com that points at O.

    Can you state in words what the "mad" part of the moment sum represents?
    You may need to consult your notes.

    Looks like "a" is the linear acceleration of the center of mass and "d" is the perpendicular-to-a distance from the pivot to the center of mass.
  4. Jan 8, 2014 #3
    Solved. Thanks
  5. Jan 8, 2014 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Well done :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted