Torque on a Non-Circular Pulley

[Axecutioner]

Homework Statement

Homework Equations

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The Attempt at a Solution

I need to find the torque (or even better, velocity) as a function of position. Right now I have mass and centroid (to find the force of gravity on the pulley at any position). Not sure if the mass moment of inertia is right. I need to know now is how the non-circularity of the pulley affects the net torque on it. I'm guessing there has to be some kind of integral of the perpendicular to the surface of the pulley but I'm not sure. Of course, this will have to be split up into 2 phases - when the cable isn't tangent to the pulley and after it is.

Any ideas?

 

[Valkarie]

Mass of the pulley: mCentroid: cRadius of the pulley: RMass moment of inertia: I = (1/2)*m*R^2Force of gravity on pulley: Fg = m*gThe net torque on the pulley will be equal to the sum of the torques due to the force of gravity, the tension on the cable, and any other external forces. The torque due to the force of gravity is simply I*Fg, where I is the mass moment of inertia of the pulley. The torque due to the cable tension is equal to the tension multiplied by the lever arm (the perpendicular distance from the centroid to the point at which the cable is attached).The torque due to any other external forces will depend on the specific situation. If there are any such forces, then it should be possible to calculate the torque by determining the lever arm for each force and then multiplying the magnitude of each force by its respective lever arm.Once all the torques have been calculated, they can be summed to determine the total torque on the pulley. This total torque can then be used to calculate the angular acceleration of the pulley (assuming it is not already rotating at a constant rate) and thus the velocity and position as a function of time.