• Explain what is meant by "conservation of energy"
• Calculate the kinetic energy of a moving object or collection of objects (slow compared to the speed of light) 
• Calculate the potential energy of an object in a uniform gravitational field, or of a stretched or compressed spring (solid)
• Describe the relation between thermal energy and kinetic energy
• Compare the potential energy of two configurations to decide which is higher
• To evaluate whether mechanical energy is conserved in specific scenarios
• To use conservation of mechanical energy to determine final velocities or configurations in situations where it applies
• To use conservation of energy together with conservation of momentum to determine final velocities of objects in elastic collisions in terms of their initial velocities.

• Describe qualitiatively the types of energy transfer occurring in various physical processes
• Calculate the energy expended in a certain process given the applied force at each location (whether the force is parallel to the displacement or in a different direction).
• Calculate the force on an object due to a spatially varying potential energy
• Identify the equilibrium position of an object given its potential energy as a function of position

RELATIVITY

Newton’s Laws and Relativity

• explain what is meant by the principle of relativity
• explain what is meant by a “frame of reference” and an “inertial frame”
• give examples of how relativity manifests itself in ordinary situations
• explain why the equivalence of physical laws in different frames implies that it is impossible to set up an experiment to measure an absolute velocity

Length contraction, time dilation, and the relativity of simultaneity

• state Einstein’s principle relativity 
• explain why Einstein's principle implies that all observers should measure the same speed for any light or electromagnetic radiation
  
• explain how a given observer can set up a coordinate system for making measurements of time and position
• be able to describe what is meant by an event
  
• give simple examples to show how Einstein's principle of relativity imply that observers at large relative velocities will not agree on distances, time intervals or whether two events are simultaneous
• describe qualitatively the meaning of length contraction, time dilation, and the relativity of simultenaity
• correctly calculate the lengths and times differences that an observer will measure, properly accounting for length contraction and/or time dilation.
• analyze basic scenarios involving large velocities to calculate times and distances for various events, or physically relevant time/distance intervals. Know when basic length contraction and time dilation formulae are applicable.
  
• be able to calculate relativistic effects in cases when velocities are much smaller than the speed of light, using Taylor (binomial) approximations to the exact formulae 

Relativistic Energy and Momentum

• argue why classical formulae for momentum and energy must be modified
• state the relativistic formulae for energy and momentum
• explain the precise meaning of conservation of energy and conservation of momentum
  
• analyze high-energy particle decay processes or collision processes using energy and momentum conservation
• provide a definition for mass in terms of energy, and apply this to make predictions about the masses of stable and unstable bound states relative to the masses of their constituents
• determine the mass of an object given its energy and momentum
  
• explain why the conservation of mass can be violated in relativistic dynamics
  
• give evidence for and explain basic implications of the equivalence between energy and mass

• Determine the center of mass of an object in various simple cases (e.g. when the object is a combination of parts with equal )
• Explain how the center of mass of an object will move given the forces on the object.

• Explain what is meant by angular position, angular velocity, and angular acceleration and describe the relation between these.
• Calculate angular velocity and/or acceleration given the angular position as a function of time.
• Calculate angular position as a function of time given the angular acceleration as a function of time and initial angular position and angular velocity.
• Qualitatively describe the rotational motion of an object given a description of its angular velocity and/or angular acceleration as a function of time.
• Translate between graphs of angular position versus time, angular velocity versus time, and angular acceleration versus time.
• Calculate the velocity of some point on an object rotating around an axis given the angular velocity.
• Determine how the linear motion of an object is related to the rotational motion of another object to which it is connected (e.g. by a rope wound around the rotating object)

• Calculate the angular momentum of an object rotation around a fixed axis
• Explain qualitatively how one can tell which of two objects has a higher moment of inertia
• Explain how one could determine the relative moment of inertia of two objects (by a direct experiment)
• Explain what is meant by "conservation of angular momentum"
• Use angular momentum conservation to determine the final angular speed of a rotating object that undergoes a change in its moment of inertia.
• Use angular momentum conservation to deduce the final rotational velocity of an object formed from an inelastic collision of two objects.
• To evaluate whether angular momentum is conserved in a given situation

• To calculate the net torque on an object in various simple situations, given the forces acting on the object (or given enough information to determine these forces)
• To determine the angular acceleration of an object given the net torque 
• To find the future angular positions and/or velocities of an object given the initial position and velocity when the torques are constant or specific functions of time.