Rotation and Linear Motion BonuS Help

[choi626]

1. 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.

2. Homework Equations

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

3. The Attempt at a Solution

Wi - friction = I (alpha)

what do i use for Inertia?

 

[Jhero]

you would use the equation for rotational inertia, which is given by I = mr^2, where m is the mass and r is the distance from the axis of rotation. In this case, you have two disks with different masses and distances from the axis P, so you would need to calculate the individual inertias for each disk and then add them together to get the total inertia for the system.

Once you have the inertia, you can use the equation for torque, which is given by T = I * alpha, to calculate the frictional torque acting on the system. This torque is what is causing the system to slow down and eventually come to rest.

To find the time at which the system will come to rest, you can use the equation Wf = Wi + (alpha)t, where Wf is the final angular velocity (which is zero when the system comes to rest), Wi is the initial angular velocity, and alpha is the angular acceleration. You can rearrange this equation to solve for t, giving you the expression for the time T at which the system will come to rest.

Overall, your solution should include the calculation of the individual inertias for each disk, the addition of these inertias to find the total inertia for the system, the use of the torque equation to find the frictional torque, and the use of the angular velocity equation to find the time at which the system comes to rest. You can then plug in the given values for u, m, L, g, and Wi to get your final expressions for a) the frictional torque and b) the time T.