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!

Acceleration of a mass connected to 2 different disks

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    The attachment gives the setup, but I can do the first part (a). The second question (not in the attachment) is "Now consider the same system as part (a) except M = .250 kg. After the system is released from rest, what will the acceleration of the .250kg mass be?

    2. Relevant equations
    sum of torques = T1*(r1) - T2*(r2) = I*angular acceleration
    sum of forces on M= Mg-T1=Ma
    sum of forces on m = T2-mg=ma

    3. The attempt at a solution
    I multiplied the two force equation by the r of the disk that each mass is attached to, then added all three equations together. The tensions cancel, giving:
    RMg-rmg = RMa + rma + I*ang acc

    I don't know what to do from here though. Maybe I = I big disk + I small disk. I don't know what ang acc is though. I would usually set it to a/r, but there are two different r's in this case. Any help is greatly appreciated!

    Attached Files:

  2. jcsd
  3. Dec 9, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Careful! The masses have different accelerations. How do the accelerations relate?


    Good--there are two different accelerations, also. :wink:
  4. Dec 9, 2008 #3
    Let's see.

    Is it Ma = MR(ang acc)
    ma = mr(ang acc)?

    If so, does the final equation, after adding all three, look like:

    g(RM + rm) = ang acc (R(^2)M + r(^2)m + .5MR(^2) + .5mr(^2) ?

    If so, you can calculate ang acceleration. Then do you just multiply that by R to get a of block 1?

    edit: actually the final equation should be (I think)
    g(RM - rm) = ang acc (R(^2)M + r(^2)m + .5MR(^2) + .5mr(^2)

    oh boy, edit again. the M and m next to .5 should be masses of the disks
    Last edited: Dec 9, 2008
  5. Dec 9, 2008 #4

    Doc Al

    User Avatar

    Staff: Mentor

    That looks OK. (Except for using the same letters to represent different masses!)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Acceleration of a mass connected to 2 different disks