Rotation and Linear Bonus Problem Help

[choi626]

Homework Statement

A system consists off two small disks of masses m and 2m that are on a plane. The length that connects the two mass is of negligible mass is is 3L long. The rod is free to rotate on a vertical axis P and the mass 2m lies L away from P and the mass m lies 2L away from P. The two disks rest on a horizontal surface and the coefficient of friction is U. At time t = 0, the rod has an initial counterclockwise angular velocity of Wi about P. The system is gradually brought to rest by friction. develop expressions for the following in terms of u, m, L, g, and Wi.
a) the frictional torque acting on the system about axis P
b) the time T at which the system will come to rest.

Homework Equations

T=I(alpha)
Wf= Wi + (alpha)t
0 = Wi + (alpha)t

The Attempt at a Solution

Wi - friction = I (alpha)

what do i use for Inertia?

 

[denverdoc]

If I'm seeing this problem right: you have a dumbell with a bar of neglible mass rotating about a center of mass right where one would compute it. You need an eqn for moment of inertia, assuming m1 and m2 are point masses. Thats what's missing and what you are asking about.

 

[choi626]

o okay so u use the parallel axis theorom plus the inertia of the two masses from Point P or the center of mass of dumbell bar?

 

[denverdoc]

well since you're computing about the CM, not sure that the parallel axis theorum enters it, but I suspect you got the right idea. sums of MR^2

 

[choi626]

thanx for replying. Does anyone have an idea how to find time. my teacher gave me a hint in saying use a angular kinemaics equation, the one i wrote along with the problem.

more info on how to confidently do part a would be appreciated but thanks for replyin

 

[denverdoc]

last post for the night, so assuming you have computed I by summing the two masses times their radii squared, you have a situation that is analogous to a block of mass M moving at an initial velocity of V and subject to a retarding acceleration of Mg*u,

only here you need to look at the retarding torque which are the sum of the frictional forces times their respective moments/I. Thats the question in (a).

Once there, it becomes a V(t)=Vo+at type of problem as you suggest.