The law of conservation of momentum states that in any closed system (including the universe) the total quantity of momentum is constant. Momentum can be transferred from one body to another, but none is lost or gained. If a system has its momentum changed from the outside it is caused by an impulse, which transfers momentum from one body to another.
When any two bodies in the universe interact, they can exchange energy, momentum, or both. The law of conservation of energy states that in any closed system (including the universe) the total quantity of energy remains fixed. Energy is transferred from one form to another, but not lost or gained. If energy is put into a system from the outside or vice versa it is often in the form of work, which is a transfer of energy between bodies.
Key Equations and Definitions
Energy⎧⎩⎨⎪⎪K=12mv2Ug=mghUspring=12k(Δx)2Kinetic energy (in Joules, kg m2s2)Gravitational potential energy, JSpring potential energy, J
Transfers⎧⎩⎨⎪⎪W=F⋅dP=ΔEΔtJ=Δp=FΔtWork is the dot product of force and displacementPower is the rate of change of energy of a system, in Watts \ (J/s)Impulse is the change in a system's momentum
Conservation Laws⎧⎩⎨∑pinitial=∑pfinal∑Einitial=∑Efinal∑Kinitial=∑KfinalTotal momentum is constant in closed systemsTotal energy is constant in closed systemsKinetic energy conserved only in elastic collisions