Work done equals force times displacement times the cosine of the angle between them, measured in joules. The work-energy theorem states that net work by all forces equals the change in kinetic energy of the body. Kinetic energy equals half the product of mass and the square of speed, and also equals momentum squared divided by twice the mass. Gravitational potential energy equals mass times acceleration due to gravity times height, referenced to an arbitrary zero level. Spring potential energy equals half the spring constant times the square of extension or compression. Mechanical energy (KE + PE) is conserved only when all acting forces are conservative — friction destroys this conservation. Power is the rate of doing work and equals force times velocity times the cosine of their included angle, in watts. For a body on a string completing a vertical circle, the minimum speed at the top is the square root of gR and at the bottom is the square root of 5gR. For a rigid rod, the body can have zero speed at the top, so the minimum bottom speed reduces to the square root of 4gR. In all collisions momentum is conserved, but kinetic energy is conserved only in elastic collisions (e = 1), while in perfectly inelastic collisions (e = 0) the bodies stick together and kinetic energy loss is maximum.