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!

Force in relation to angular momentum

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

    so a student is sitting on a spinning stool and has a 2kg dumbbell in each hand angular velocity is 3rad/sec arms stretched out is a radius of 80cm and he pulls in his arms to 20cm. for this problem your ignoring the students weight.

    from other problems i have figured out
    so angular velocity to start with is 3 rad/sec
    angular velocity final is 48 rad/sec

    kinetic energy initial is 11.52( dont know what this dimensions is so im guessing J)
    kinetic energy final is 184.32
    angular momentum = 7.68

    and i need to find the force required to pull one of the dumbbells in at a constant speed is equal to F=((initial angular momentum of 1 block)^2)/(4*Mass of one weight*Radius^3))

    2. Relevant equations

    3. The attempt at a solution
    do i say Torque=F*d and Torque=I*alpha and then go Force = Ia/d? or is there another way to solve this that im not seeing ?
    or do i use the change in kinetic energy equation 1/2*I*[tex]\omega[/tex]^2Final-1/2*I*[tex]\omega[/tex]^2initial = F*d
    Last edited: Oct 28, 2010
  2. jcsd
  3. Oct 28, 2010 #2


    User Avatar
    Homework Helper

    I would think the change in kinetic energy would be equal to the work done in moving the dumbell from 80cm to 20 cm.
  4. Oct 28, 2010 #3
    Yes, KE would increase when moved from 80cm to 20cm. It would increase 16 times!

    The KE is gained at the expense of work done overcoming the radial inertial force (m * w^2 * r) along a distance 60 cms. w = angular velocity. As the dumbell is moving from 80 to 20, the angular velocity increases to satisfy the angular momentum conservation. So "w" at any radial distance is given by w(r) = w(R) * (R/r)^2

    where w(R) is the angular velocity at radius R. If we put this inertial force and work done in moving infinitesimal distance "dr" then we get a definite integral that gives the work done to increase the KE from bringing the dumbell from 80cms to 20cms
    Last edited: Oct 28, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook