Energy
A scalar quantity representing the capacity to do work or transfer between forms (motion, position, heat, etc.). Measured in joules (J). Conserved in all interactions.
FoundationJoule (J)
The SI unit of energy and work. 1 J = 1 N·m (one newton times one meter). Equivalent to the energy needed to lift a 100 g apple about 1 meter.
FoundationKinetic Energy
The energy an object has because of its motion. Always positive (or zero). A scalar.
3.1 Translational KETranslational Kinetic Energy
K = ½mv². The kinetic energy due to motion of an object's center of mass. (Rotational KE comes in Unit 6.) Doubling speed quadruples KE — speed appears squared.
3.1 Translational KEReference-Frame Dependence of KE
Kinetic energy depends on the observer's reference frame, because velocity does. A person on a train has zero KE in the train's frame but lots of KE in the ground frame.
3.1 Translational KEWork
W = F·d·cos(θ). The energy transferred to or from a system by a force acting over a distance. A scalar that can be positive (force aligned with motion), negative (force opposes motion), or zero (force perpendicular to motion).
3.2 WorkNet Work
The sum of work done by ALL forces on an object. By the work-energy theorem, net work equals the change in kinetic energy: W_net = ΔK.
3.2 WorkWork-Energy Theorem
The net work done on an object equals its change in kinetic energy: W_net = ΔK = ½mv_f² − ½mv_i². A powerful shortcut — sometimes faster than F = ma + kinematics.
3.2 WorkConservative Force
A force whose work depends only on the starting and ending positions, NOT the path taken. Examples: gravity, spring force. If you return to your starting point, conservative forces do zero net work overall.
3.2 WorkNon-Conservative Force
A force whose work depends on the path taken. Examples: friction, air drag. These forces dissipate mechanical energy — typically into thermal energy or sound.
3.2 WorkPath-Dependent vs Path-Independent
Work done by conservative forces is path-independent (only start and end matter). Work done by non-conservative forces is path-dependent (a longer path with friction wastes more energy).
3.2 WorkForce-Displacement Graph
A graph of force vs. position. The AREA under the curve equals the work done by that force. Useful for non-constant forces like a spring stretching.
3.2 WorkPotential Energy
Stored energy due to the position or configuration of objects in a system. A scalar. Only conservative forces have associated potential energies. The zero of PE is arbitrary — you pick where it's zero.
3.3 Potential EnergyGravitational PE (near surface)
U_g = mgh, where h is the height above your chosen zero level. Works well near Earth's surface where g is nearly constant. Bigger h means more stored gravitational energy.
3.3 Potential EnergyUniversal Gravitational PE
U_g = −Gm₁m₂/r. Used for objects far apart (planets, satellites). Notice the NEGATIVE sign: gravitational PE is most negative when objects are closest, and approaches zero as r → ∞.
3.3 Potential EnergyElastic Potential Energy
U_s = ½kx². The energy stored in a stretched or compressed spring, where x is the displacement from equilibrium and k is the spring constant. Always positive.
3.3 Potential EnergyReference Point (Zero of PE)
The position you choose to call h = 0 (or x = 0). PE is always relative to this choice. The CHANGE in PE is what matters physically — so pick a zero that simplifies the problem (often the lowest point).
3.3 Potential EnergyMechanical Energy
ME = K + U. The sum of an object's (or system's) kinetic and potential energies. The total of "useful" energy in the mechanical world before any becomes heat or sound.
3.4 Conservation of EnergyConservation of Energy
In any interaction, total energy is constant. Energy is never created or destroyed; it only moves between systems or transforms between forms. Universal law — no known exceptions.
3.4 Conservation of EnergyConservation of Mechanical Energy
When only conservative forces (gravity, springs) do work on a system, ME stays constant: K_i + U_i = K_f + U_f. Use this when no friction or applied external work changes the system.
3.4 Conservation of EnergyEnergy Transfer
Energy moving from one system to another (e.g., your hand pushing a box transfers energy to the box). Work is one common mechanism of energy transfer.
3.4 Conservation of EnergyEnergy Dissipation
The conversion of mechanical energy (KE + PE) into thermal energy, sound, or other forms — usually via friction or drag. Dissipated energy can no longer do mechanical work in the system.
3.4 Conservation of EnergyThermal Energy
Random microscopic kinetic energy of particles in an object. When friction acts, the lost mechanical energy usually becomes thermal energy — the surfaces get warmer.
3.4 Conservation of EnergyClosed (Isolated) System
A system with no energy entering or leaving. Total energy is constant. The choice of system matters — if you include all parts (block + ramp + Earth), even friction-laden situations can be analyzed by including thermal energy.
3.4 Conservation of EnergyPower
The rate at which energy is transferred or transformed: P = ΔE/Δt. A scalar. SI unit: watt (W = J/s). Two systems can transfer the same total energy, but the one that does it faster has more power.
3.5 PowerAverage Power
P_avg = ΔE/Δt. The total energy transferred divided by the total time. Like an "average velocity" of energy delivery.
3.5 PowerInstantaneous Power
Power at a single instant. For a constant force pushing an object at velocity v, P = F·v (when F and v are in the same direction). Useful for engines and motors.
3.5 PowerWatt (W)
The SI unit of power. 1 W = 1 J/s. A 100 W lightbulb dissipates 100 joules of energy every second. 1 horsepower ≈ 746 W.
3.5 Power