Linear momentum is the product of an object's mass and its velocity, written as \(\vec{p} = m\vec{v}\), and is a vector quantity whose direction matches the direction of motion. When a net force acts on an object, the change in momentum over a time interval equals the impulse delivered. In any closed system where no external forces act, the total linear momentum is conserved. This principle is invaluable for analyzing collisions, where the combined momentum of the colliding objects before the event equals the combined momentum after.
When an object moves in a circle at constant speed, the motion is called uniform circular motion. Even though the speed is constant, the direction of the velocity changes continuously, so the object is accelerating. This centripetal acceleration is directed toward the center of the circle and has magnitude \(a_c = v^2/r\). The force responsible for this acceleration, the centripetal force, is also directed toward the center and is provided by some real physical interaction such as tension, gravity, or friction.
Rotational motion has its own set of quantities analogous to those in linear motion. Torque is the rotational equivalent of force, given by \(\tau = rF\sin\theta\), and is the cause of angular acceleration. The moment of inertia \(I\) plays the role of mass for rotation, defined for a collection of point masses as \(I = \sum m r^2\), where each \(r\) is the perpendicular distance from the axis of rotation. Angular momentum, \(L = I\omega\) for a rigid body or \(L = r \times p\) more generally, is conserved whenever no external torque acts on a system. Pressure in fluids is defined as force per unit area, \(P = F/A\), and acts equally in all directions at a point in the fluid. Archimedes' principle states that the buoyant force on a submerged or floating object equals the weight of the fluid displaced; an object floats when the buoyant force is at least equal to its weight.