How Is Angular Velocity Affected by Torque in a Multi-Pulley System?

[Yapper]

Homework Statement

Q2: IF mA=2kg, mB=7kg, and mC=5kg. Starting from rest, if a torque of 5Nm is
given at t=0 to pulley A about point A for 3 seconds. Determine the angular
velocity of the 3 pulleys at t=3s.

[PLAIN]http://img98.imageshack.us/img98/8214/unled2tw.png

Homework Equations

relationship between rotational velocity and radius of 2 linked pulleys:
wa/wb = ra/rb

moment of inertia for a pulley:
I = 1/2mr^2

torque and angular acceleration:
t = Iα

The Attempt at a Solution

I calculated the moments of inertias for all 3 pulleys but I don't know how to apply them with the torque. Do I just add all 3 of them together and put it into t=Iα to find the acceleration and then figure out the velocity after 3 seconds? Thanks

 

[tiny-tim]

Hi Yapper!

(have an omega: ω and a tau: τ and try using the X² and X₂ icons just above the Reply box )

I calculated the moments of inertias for all 3 pulleys but I don't know how to apply them with the torque. Do I just add all 3 of them together and put it into t=Iα to find the acceleration and then figure out the velocity after 3 seconds?

nooo, don't be laaazy …

call the tensions T₁ and T₂, and do τ = Iα for each of the three pulleys (separately).

 

[Yapper]

Thanks ill give it a try

 

[tiny-tim]

actually, thinking again, there is a lazy way to do this problem …

(but it involves a bit of calculus at the end)

call the angle the first pulley goes through θ_A,

then find the work done as a function of θ_A, and equate that to the kinetic energy of all three pulleys, giving a differential equation relating θ_A and dθ_A/dt, from which you can find θ_A or dθ_A/dt as a function of t without finding the tensions …

try it both ways, to see ​