Q: How do we know if/when an object’s momentum has changed? Or do we always assume it’s constant because of the Law of Conservation of Momentum? Are there any special cases where this doesn’t apply?
A: According to the Impulse-Momentum Theorem, the momentum of an object or a system (multiple objects) changes if an impulse is applied. Practically, in two types of set-up, the impulse is considered zero and the momentum is conserved.
1, An object/system which has no force or zero net force applied on. For example, an object is doing a uniform motion on a frictionless surface.
2, An object/system which has non-zero net force applied on, but net force is small and lasts for a very short (negligible) time interval. For example, two balls collide on a rough surface. The friction force on the system (2 balls) is small compared to the internal force between balls and the time duration is very short.
In other cases, for example, in a projectile motion (neither force nor time duration can be neglected), the impulse is non-zero and the momentum is not conserved!
Q: For an object in a 2-D motion with constant speed, is the net force in the direction of velocity zero or non-zero?
A: The net force in the direction of velocity only affects the magnitude of velocity (speed) while the net force perpendicular to the the direction of velocity only affects the direction of velocity. Therefore, in a 2-D motion with constant speed, for example, a Uniform Circular Motion, the net force in the direction of velocity is zero (corresponding to constant speed) and the net force perpendicular to the the direction of velocity is non-zero (corresponding to 2-D).
