• Motion energy is properly called kinetic energy; it is proportional to the mass of the moving object and grows with the square of its speed. (6-8)
• A system of objects may also contain stored (potential) energy, depending on their relative positions. (6-8)
• Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system's total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (9-12)

• Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system. (9-12)
• Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (9-12)
• Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior. (9-12)

• When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. (6-8)

• The transfer of energy can be tracked as energy flows through a natural system. (6-8)
• The total amount of energy and matter in closed systems is conserved. (9-12)
• Changes of energy and matter in a system can be described in terms of energy and matter flows into, out of, and within that system. (9-12)
• Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems. (9-12)

• 6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.
• 9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.
• 9-12: 4E/H3. As energy spreads out, whether by conduction, convection, or radiation, the total amount of energy stays the same. However, since it is spread out, less can be done with it.
• 9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.
• 9-12: 4E/H10. If no energy is transferred into or out of a system, the total energy of all the different forms in the system will not change, no matter what gradual or violent changes actually occur within the system.

• 9-12: 11C/H10. Whatever happens within a system, such as parts exploding, decaying, or reorganizing, some features, such as the total amount of matter and energy, remain precisely the same.

• N-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
• N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

• F-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for ?/3, ?/4 and ?/6, and use the unit circle to express the values of sine, cosine, and tangent for ?—x, ?+x, and 2?—x in terms of their values for x, where x is any real number.

• G-SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

• RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11—12 texts and topics.

• RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

This five-part tutorial helps users analyze motion from the perspective of Work and Energy.  Explore potential energy, kinetic energy, and total mechanical energy with the help of descriptive text, sample problems with solutions, force diagrams, and links to related animations. Resource was designed for students of high school physics, but could also be very useful as a refresher for middle school teachers.

• Physical Sciences K-8 Teaching About Energy Unit
• Physics First Teaching About Energy Unit
• Conceptual Physics Teaching About Energy Unit
• Algebra-Based Physics Teaching About Energy Unit
• AP/Calculus-Based Physics Teaching About Energy Unit

In this five-part tutorial you will explore potential energy, kinetic energy, and total mechanical energy with the help of sample problems and solutions, force diagrams, and links to related animations. This tutorial is appropriate for secondary science teachers and for students of high school physics.

• Physical Sciences K-8 Conservation of Energy Unit
• Physics First Conservation of Energy Unit
• Conceptual Physics Conservation of Energy Unit
• Algebra-Based Physics Conservation of Energy Unit
• AP/Calculus-Based Physics Conservation of Energy Unit