Need some help with Rotational Physics and determining angular velocity.

[Akira__tyler]

Alright, so I am a programmer. I am writing a physics engine for a project at school and I am having a lot of trouble understanding rotational physics. As of now, the tools I have to work with are the point of collision for an object, it's velocity, it's acceleration (gravity), and it's center of mass. What I don't understand is how to get the angular velocity from this data, and how this velocity is related to the point of collision and the center of mass of the object?

Assume that the object is a rectangle and that the center of mass is located in the center of an object of length 20 and height 2. It's mass is 50(kg if you want). If the object falls onto the tip of a triangle located at a horizontal offset of 3 from the center of mass, how do I find the angular velocity and how would the angular velocity change if I moved the point of collision?

The main thing I am looking for is to understand the application of any formulas there are, as well as why they work the way they do. Sorry if this question is a bit weird, but I could use any help at all really. Thanks.

 

[ACPower]

You want to calculate the torque, the rotational equivalent of a force, that arises when the collision occurs and the Center of Mass starts rotating around the point of impact, which is (temporarily) fixed. The magnitude of the torque is the change in angular momentum, and is the force times the distance between the C.o.M. and the new pivot. You could probably get the instantaneous angular velocity by multiplying the velocity perpendicular to the line between C.o.M. and pivot by its length...

 

[Akira__tyler]

Thanks for the help, that cleared up most of what I was confused about. I guess I just needed some help visualizing what I needed to do. There is one part of your explanation that I am still a bit confused about though and that was about calculating the instantaneous angular velocity. I tried drawing a force diagram, but still couldn't quite figure it out.

Does that instantaneous angular velocity have any effect on any forces on the object besides rotational forces? Or is it kind of like it's own independent system with respect to the object?

 

[ACPower]

My 'Instantaneous Angular Velocity' is probably a non-rigorous bookkeeping trick. I would try to just take the linear velocity of the CoM just before contact and use it for the angular velocity, which would just be V/r. You should probably use just the component of the linear velocity perpendicular to to the torque arm divided by the length of the torque arm as the angular velocity part, and keep the parallel component in your linear velocity...

 

[Akira__tyler]

Perfect, that's exactly what I needed. Thanks.