Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Moment of Inertia - center of a rod w/ unequal distribution

  1. Dec 5, 2014 #1
    Hello everyone!

    New member here, as an ME major I always seem to come across very valuable information here, so I figured I would see if possibly someone here could help me.

    The problem I am dealing with involves modeling a car through certain motions such as hitting a speed bump, and part of this is finding the moment of inertia.

    The vehicle weight distribution is as follows;
    Total Weight = 2063.85 kg

    Weight Distributions;
    Front = 57.9% = 1194.97 kg
    Rear = 42.1% = 868.88 kg

    I'll try and ask this as clear as possible, please bear with me.

    I am confused when it comes to evaluating this. Assume that I am correct in creating a simple model by modeling it as a rod (1/12)(m)(l^2). I am not sure if I should use the center of the overall length, combined with the parallel axis theorem, or if I should be looking more into the radius of gyration. Also, when using these, should I determine first the center of gravity for the weight distribution (making l1 > l2), and then solve with those values?

    Any and all input is very much appreciated, I feel as though I am very close but I am definitely missing some key differences between the methods. I have included a simple diagram to aid in visualizing my problem statement.

    project drawing (772 x 600).png
  2. jcsd
  3. Dec 5, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Cars are not very rod-like. Their mass is not only distributed longitudinally, but to a certain extent, vertically and transversely as well.

    Things like engines and transmissions represent concentrations of mass which are a significant fraction of the total mass of the vehicle. The radius of gyration would be a more appropriate piece of information to use to develop the MOI of a complex machine like a car.

    The radius of gyration is typically calculated using the MOI about the c.g., so you should also know where the c.g. of the vehicle is located. The F/R weight distribution will give you one coordinate of the c.g.; you'll have to estimate the other two.
  4. Dec 5, 2014 #3
    Thank you for your input SteamKing.

    I understand that cars are much more complex than just a rod, however this simulation is "basic" simulation which will be created using Simulink.

    The parameters I provided were referenced from Jeep handbooks as 56/44 (%, F/R dist.). After accounting for the additional weights, summing forces and moments, I came up with the seemingly reasonable new value of 57.9% and 42.1%.

    It sounds like I would want to use the radius of gyration method for this problem, but what do you mean the F/R Distribution will give me one, but I'll have to estimate the other two? I assume you're talking about treating the front and rear of the vehicle as something like a point mass or distributed load, some distance away?
  5. Dec 5, 2014 #4
    (Attachment in aid to my previous post)
  6. Dec 5, 2014 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    What I meant was that the F/R weight distribution will give you the longitudinal location of the center of gravity, not the radius of gyration. The gyradius can be different for different cars with the same F/R weight distribution.

    The gyradius is either given as a distance (in feet or meters, for example) or as a percentage of length, width,or height of the car, depending on which MOI you are interested in.
  7. Dec 5, 2014 #6
    Okay, thank you very much!

    Would you (or anyone else) be able to steer me in the right direction of finding the MOI about the center of gravity under the conditions I have provided?

    Once again, thank you very much for all of your help, I appreciate it immensely.
  8. Dec 5, 2014 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Further to your quest for calculating the MOI of anything, there is a class of engineer, formerly called weight engineers, whose specialty it was to do a weight take-off of a vehicle, whether it was an automobile, airplane, spacecraft, ship, whatever, where the total weight, c.g., and inertia properties were critical to the proper design of the machine.

    Now, you could make a rough weight take-off estimate of the MOI of your vehicle by looking at the major weight groups, like the engine, transmission, wheels and tires, suspension parts, body & frame, etc. As an ME major, I'm somewhat surprised that you haven't had to do such a calculation as part of your training.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook