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!

Rotational kinematics (mass wrapped around inner hub)

  1. Dec 10, 2014 #1
    1. The problem statement, all variables and given/known data
    A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of
    6.55 kg, a radius of R = 38.0 cm and is in the shape of a ring. A mass M = 1.85 kg is attached to
    the end of a string which is wrapped around an inner hub which has a radius r = 5.40 cm.

    Initially, the mass M is a distance h = 72.0 cm above the floor. [Assume friction is negligible!]
    a. What will be the resulting angular acceleration of this wheel?
    b. How long will it take for the mass M to reach the floor?
    c. What will be the total angular displacement of the wheel during the time in which the mass M
    is falling to the floor?
    d. How much work was done on the wheel by the external torque as the mass M falls to the floor?

    2. Relevant equations
    torque = FR = I * alpha
    F = Ma
    a = alpha * r

    I = mr^2 (told to ignore the spokes of wheel, same as hoop)
    3. The attempt at a solution
    I tried using T*R = I * alpha (T = tension, I = mR^2 where m is mass of wheel)
    and Mg - Ma = T and a = alpha *r

    I substituted for T, combined them together to solve for alpha,
    got alpha = MgR/(mR^2 + MR^2)
    which is 5.795

    however answer is 1.06rad/s^2. Can you help?
     
  2. jcsd
  3. Dec 10, 2014 #2

    jbriggs444

    User Avatar
    Science Advisor

    T*R = I*alpha? If I understand the problem description correctly, the tension T acts at a distance r from the hub, not R.

    That would explain why the answer you derived is independent of r while the real answer should depend strongly on r.
     
  4. Dec 10, 2014 #3
    that did it thanks! Mgr/(MR^2 + Mr^2) got me the answer
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rotational kinematics (mass wrapped around inner hub)
Loading...