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Angular Acceleration, 2 Pulleys on common axle

  1. Apr 19, 2009 #1
    Note: This is similar to 2 previous questions I've seen here (https://www.physicsforums.com/showthread.php?t=261193"), and while this is my first post, I've lurked/found this site to really be helpful in getting me to be able to figure out how to solve problems I have with my physics homework.

    1. The problem statement, all variables and given/known data

    Two pulley wheels, one of radius 0.3 m and the other of radius 0.82 m, are mounted rigidly on a common axle. The rotational intertia of the two pulleys, which are clamped together, is 3.3 kg·m². A mass of 44 kg mass is attached on the left and a mass of 37 kg mass on the right, as shown.

    attachment.php?attachmentid=15717&d=1222991526.jpg

    Find the angular acceleration of the system. Take the clockwise direction to be positive. The acceleration of gravity is 9.8 m/s². Answer in units of rad/s².

    2. Relevant equations

    ΣΤ = Iα

    ΣΤ = Τ1 + Τ2

    3. The attempt at a solution

    So, the process I followed was this:

    I found the torques for each mass & radius:

    Τ1 = -(m1)g(R1)sin(90) --> (negative because going CCW)

    Τ2 = (m2)g(R2)sin(90) --> (positive because going CW)

    Therefore: ΣΤ = (m2)g(R2) - (m1)g(R1) = g(m2R2 - m1R1)

    Which means: g(m2R2 - m1R1) = Iα

    α = g(m2R2 - m1R1)/I

    Checking the units, I should get rad/s²:

    m/s²·(kg·m)/kg·m²

    Which is: (m²·kg)/(s²·kg·m²)

    Results in: rad/s²

    So my units check out.

    So, with the following variables (I'm hoping I got the left/right values correct):

    • g = 9.8 m/s²
    • m1 = 44 kg
    • R1 = 0.3 m
    • m2 = 37 kg
    • R2 = 0.82 m
    • I = 3.3 kg·m²

    Plugging these in, I get:

    α = [9.8]([37][0.82] - [44][0.3])/[3.3]

    α = (9.8)(30.34 - 13.2)/3.3

    α = (9.8)(17.14)/3.3

    α = (167.972)/3.3

    α = (167.972)/3.3

    α = 50.90060606 rad/s²

    Which, apparently, is wrong. So I'm at a loss. What did I do wrong? Or rather, what would be a good hint for me to figure out where I went wrong?

    (and yes, I know it seems strange for an α > g... that doesn't seem to logically follow for me)
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Apr 19, 2009 #2

    LowlyPion

    User Avatar
    Homework Helper

    Welcome to PF.

    Did you enter just 50.9?
     
  4. Apr 19, 2009 #3
    No, but the homework system my teacher uses is very annoying in needing an incredible number of sig figs. So I always have to just leave everything my calculator prints out to have success.

    Update: Yes. It didn't help. I'm apparently missing something in my calculations.
     
    Last edited: Apr 19, 2009
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