# Dynamic rotation

1. Nov 29, 2006

### inner08

1. The problem statement, all variables and given/known data
Two blocks of mass m1=3kg and m2=5kg are linked by a cord passing through a pulley of radius R=8cm and of mass M=4kg. We neglect friction and we assimilate the pulley to a disk. We place the origin at the center of the pulley.

a) what is the total torque on the system?
b) what is the kinetic moment (I hope I translated it correctly..its moment cinetique in french) of the system when the blocks have a speed of v?
c) Find the acceleration of the blocs by applying the equation torque(ext)=dL/dt.

2. Relevant equations
torque(ext)=dL/dt
T1-T2= Ia
a = alpha * r

3. The attempt at a solution

I drew a fbd and came up with this:

m1: T1-m1*g=m1*a
m2: m2*g - T2 = m2*a
pulley: T2 - T1 = I(alpha)

I figured i'd try to isolate alpha and then substitute it in the equation T1-T2 to find the torque.

m2*g - m2*a - (m1*a + m1*g) = I * alpha
5 * 9.8 - 5a - 3a - 3*9.8 = (1/2)MR^2 * alpha
49 - 8a - 29.4 = (1/2)4*0.08^2 * alpha
19.6 - 8a = 0.0128 * alpha
19.6 - 8(alpha*r) = 0.0128 *alpha
19.6 - .64alpha = 0.0128alpha
19.6 = 0,6528alpha
alpha = 30

Substitute alpha in the equation torque = T2 - T1

19.6 - .64 * 30 = 0.4 <-- this is wrong..it should be 1.57

2. Nov 29, 2006

### OlderDan

You are being asked for the torque acting on the system, not the torque acting on the wheel. This problem is a but unusual. It wants you to look at the angular momentum of the whole system relative to the origin and the effect of external torques acting on that system

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