Description: The work-energy theorem is derived showing that the change in kinetic energy equals the work done on a particle by the sum of all forces. Gravity does negative work on an object thrown upwards until it reaches its maximum height of its trajectory.

Description: Work in 3D is shown to decompose into the sum of each 1D component.

Description: Work done by gravity while a particle moves upwards a vertical distance h is -mgh, regardless of the path taken. When the work done by a force is independent of the path, that force is called a conservative force.

Description: Potential energy and kinetic energy can be converted back and forth but their sum, the mechanical energy, is conserved if only conservative forces are involved.

Description: The centripetal acceleration, when the roller coaster is upside down, must be greater than g; the mechanical energy must therefore exceed a threshold value.

Description: The gravitational force falls off as one over the distance squared. If large distances are involved, the gravitational potential due to an object of mass M is taken to be zero at infinity.

Description: If released with zero speed, the wrecking ball should NOT swing higher than its height when it was released. Professor Lewin puts his life on the line by demonstrating this.