Q: For conservation of momentum, what counts as an external force/impulse? Does gravity count?
A: After we have defined the system of interest in a problem, for example, the 2 objects in a 2-body collision, any force/impulse from the outside of the system is considered external! Yes, gravity is external! However, the impulse of gravity is neglected in most collisions since it is either in the direction perpendicular to the momentum/motion or small in magnitude compared to other impulses.
Q: When calculating torque, are there any instances where we use cosine instead of sine, or do we always use sine, since we are multiplying the radius by the perpendicular force acting on the object?
A: The angle we use in calculating a torque is the angle between the Force (F) vector and the lever arm (r) vector, so it always sine function in the equation. Essentially, this comes from the “Cross Product” operation of vectors. For more details, you can google it or check out my earlier post: https://www.physicsdoable.com/posts/2020-11-06-highlights-of-questionanswer/
If you use r⊥ or F⊥ in the equation of torque, the angle is 90 degrees and the sine value is 1. Thus, you can skip the sine function in the calculation. Also see the attached pictures.
