# Useful Formulae

30 ENERGY, WORKMOMENTUM conservation in action An object, mass m, moving in a straight line with velocity v has kinetic energy Ek mv2. This is energy it possesses because of its motion. When an applied force changes its velocity to u,the total workdone,W,is the change in kinetic energy W mv2 mu2 Generally, workmeasures an exchange of energy between two bodies. Someone lifting an object of mass mto a height habove its initial position does work, here transferring gravitational potential energy,Ep,to the object it can now fall. Ep mgh mg is the weight of the object,a force. When the object falls, it loses height but gains velocity, thus Ek increases as Ep decreases. Ignoring friction,the total energy of the object E Ek Ep remains constant until it lands, when its remaining kinetic energy is dissipated as heat and noise. The linear momentumof an object is given by p mv. For a point mass mrotating about an axis at distance r,the angular momentum, L equals mvr mrr mr2where is the angular velocityof the body, in radians per second. I mr2 is known as the moment of inertia. The rotational kinetic energyof a system is then Ekr I2. A general rotating solid can be treated as if it were a point mass rotating about the same axis with the appropriate radius of gyration. This is shown opposite and can be found using the methods of calculus see page 48. If no external forces act on a system,its total momentum is always conserved. 31