8.1. The Big Idea http://www.ck12.org
8.1 The Big Idea
The law ofconservation of momentumstates 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 animpulse,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 ofconser-
vation of energystates 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 ofwork,which is a transfer of energy between bodies.
Key Equations and Definitions
Energy
K=^12 mv^2 Kinetic energy (in Joules, kg m^2 s^2 )
Ug=mgh Gravitational potential energy, J
Uspring=^12 k(∆x)^2 Spring potential energy, JTransfers
W=F·d Work is the dot product of force and displacement
P=∆∆Et Power is the rate of change of energy of a system, in Watts (J/s)
J=∆p=F∆t Impulse is the change in a system’s momentumConservation Laws
∑pinitial=∑pfinal Total momentum is constant in closed systems
∑Einitial=∑Efinal Total energy is constant in closed systems
∑Kinitial=∑Kfinal Kinetic energy conserved only in elastic collisions