Anything that's moving has kinetic energy. The faster it moves or the more massive it is, the more KE it has. The formula is K = ½mv² — and the v² means KE grows fast with speed: doubling speed gives 4× the energy.
Key Properties
Formula
K = ½mv². Always positive (or zero).
Type
Scalar quantity. No direction.
Units
Joules (J) = kg·m²/s²
Frame-Dependent
Different observers measure different KE values (because they measure different v).
Example
A baseball pitcher's fastball
A 0.15 kg baseball is thrown at 40 m/s. Its kinetic energy is:
K = ½ · 0.15 · (40)² = ½ · 0.15 · 1600 = 120 J
If the pitcher throws it at 50 m/s instead, K becomes ½ · 0.15 · 2500 = 187.5 J — a 56% increase in energy for a 25% increase in speed. The v² makes a big difference.
Topic 3.2
Work
The bridge between forces and energy
The Big Idea
Work measures how much energy a force transfers to or from a system. W = F·d·cos(θ), where θ is the angle between force and displacement. Only the component of force PARALLEL to the motion counts — perpendicular forces do zero work. The work-energy theorem says: net work = change in KE (W_net = ΔK).
The Three Possibilities
Positive work (force aligns with motion) — adds energy to the object. Speed increases.
Negative work (force opposes motion) — removes energy. Speed decreases. Friction always does negative work.
Zero work (force perpendicular to motion) — no energy transferred. Normal force on a horizontally sliding block; gravity on a satellite in circular orbit.
Example
Pushing a sled across snow
You push a 20 kg sled across snow with 50 N of force at an angle of 37° above horizontal. The sled slides 10 m. How much work do you do? (cos 37° = 0.80)
W = F·d·cos(θ) = 50 · 10 · 0.80 = 400 J
If friction does −200 J of work, the net work is W_net = 400 + (−200) = 200 J. By the work-energy theorem, the sled's KE increased by 200 J.
Topic 3.3
Potential Energy
Stored energy from position
The Big Idea
Potential energy is stored energy — it depends on the position or configuration of objects in a system. Only conservative forces (gravity, springs) have associated potential energies. The zero of PE is ARBITRARY — only changes in PE matter. Three forms appear in Unit 3:
The Three Forms
Gravitational (near Earth)
U_g = mgh, where h is height above your chosen zero.
Universal Gravitational
U_g = −Gm₁m₂/r. Negative; → 0 as r → ∞.
Elastic (Spring)
U_s = ½kx². x = displacement from equilibrium.
Zero of PE
You pick where it's zero. Only ΔU matters.
Example
A book on a shelf
A 2 kg book sits 1.5 m above the floor on a shelf. Taking the floor as the zero of PE:
U_g = mgh = 2 · 10 · 1.5 = 30 J of gravitational PE
If a 200 N/m spring is also compressed by 0.10 m, it stores:
U_s = ½ · 200 · (0.10)² = 1 J of elastic PE
Both forms of stored energy are ready to convert into kinetic energy when released.
Topic 3.4
Conservation of Energy
Energy is never created or destroyed
The Big Idea
The total energy of a closed system is constant. It only moves between forms (kinetic ↔ potential ↔ thermal) or between systems. Mechanical energy (ME = K + U) is conserved when only conservative forces act. When friction or drag is present, ME drops — but the lost energy becomes thermal energy. Total energy is STILL conserved.
How to Apply It
Identify initial and final states. Where does the motion start and end?
Choose a zero of PE. Usually the lowest point.
Write the energy equation: K_i + U_i = K_f + U_f (no friction) or K_i + U_i = K_f + U_f + E_dissipated (with friction).
Solve for the unknown — often a speed or height.
Example
A ball rolls down a frictionless ramp
A 1 kg ball is released from rest at the top of a 5 m tall frictionless ramp. How fast is it going at the bottom?
Take the bottom as the zero of PE. Initial: K_i = 0, U_i = mgh = 1·10·5 = 50 J. Final: K_f = ½mv², U_f = 0.
Conservation: 0 + 50 = ½(1)v² + 0 → v² = 100 → v = 10 m/s
Notice: We never needed the ramp's angle or shape! Energy methods don't care about the path.
Topic 3.5
Power
How fast energy moves
The Big Idea
Power = energy ÷ time. Average power: P_avg = ΔE/Δt. It tells you how QUICKLY energy is transferred or transformed. Two systems can do the same total work, but the one that does it faster has more power. SI unit: watt (W = J/s).
Key Equations
Average Power
P_avg = ΔE/Δt = Work/time.
Instantaneous (constant F)
P = F·v (when F and v are aligned).
SI Unit
Watt (W) = 1 joule per second.
Comparison
100 W bulb uses 100 J every second.
Example
Climbing a flight of stairs
A 60 kg student climbs a 4 m staircase in 5 seconds. What's the student's power output?
Work done against gravity: W = mgh = 60 · 10 · 4 = 2400 J
Power: P = W/Δt = 2400 / 5 = 480 W
If the student ran up the stairs in 2.5 seconds instead, the work would be the same (2400 J), but the power would double to 960 W. Same total energy, but twice the rate of delivery.
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How to use this visual review
Take 1–2 minutes per slide. Read the Big Idea first, then the definitions, then the worked example. Five slides total — one per topic.
Use the topic pills to jump to any topic, or use the arrow keys to step through them in order.
This works well for the night before the exam — five slides is enough to refresh Unit 3 in about 10 minutes.