The terms 'conserved quantity' and 'conservation law' have specific scientific meanings in physics, which differ from the meanings associated with their everyday use. For example, in everyday usage, water could be conserved by not using it, by using less of it, or by re-using it. However, in scientific terms, a conserved quantity of a system stays constant, changes by a definite amount that is transferred to other systems, and is converted into other forms of that...

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy conservation, we study more than one body at the same time. Second, identify all forces acting on the object and determine whether each force doing work is conservative. If a non-conservative force (e.g., friction) is doing work, then mechanical energy is not conserved. The system must then be analyzed with non-conservative work. Third, for...

A system's total angular momentum remains constant if the net external torque acting on the system is zero. Considering a system that consists of n tiny particles, the angular momentum of any tiny particle may change, but the system's total angular momentum would remain constant. The principle of conservation of angular momentum only considers the net external torque acting on the system. While there are internal forces exerted by different particles within the system that also produce...

A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a...

The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its momentum to be conserved:

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this mechanical energy when only conservative forces cause energy transfers within the system—that is, when frictional and drag forces do not act on the objects in the system? Also assume that the system is isolated from its environment; in other words no external force from an object outside the system causes energy changes inside the system.
When a...