Click card to flip · Shows question / answer
Click any card to expand. Read these six in-depth sections and you'll be able to answer every Practice Q&A, Bonus, and Test question (including Test 3 on Work, Energy & Machines). Each section ends with the exact question types it unlocks.
This section is your foundation: how we describe motion, the laws that explain it, and how energy and waves fit in. Everything else in the chapter builds on these ideas.
Distance is how far you travel; displacement is the straight-line change in position from start to finish (it has a direction). Speed tells you how fast you go. Velocity is speed plus a direction, and acceleration is how quickly your velocity changes.
Here is a subtle but important idea: an object can be moving at a constant speed and still be accelerating — if its direction changes. A car going around a curve at a steady 60 mph is accelerating, because velocity (a vector) is changing. Any change in speed OR direction means the acceleration is not zero.
Sir Isaac Newton gave us three rules that explain why things move the way they do.
Gravity pulls everything toward Earth's center, giving every falling object the same acceleration, g ≈ 9.8 m/s² (often rounded to 10). Mass does not matter in free fall: with no air resistance, a bowling ball and a tennis ball dropped together hit the ground at the same time.
An object's weight is the force of gravity on it: Weight = mass × g. Weight gets smaller as you move away from Earth, because gravity follows an inverse-square law (twice as far = one-quarter the pull). Mass, however, never changes.
Energy is the ability to do work, and it comes in forms that can transform into one another.
Power is how fast work is done: Power = Work ÷ time, measured in watts. Two people who lift identical barbells do the same work, but whoever finishes faster used more power.
Momentum = mass × velocity (p = m v). It measures how hard something is to stop. Momentum is always conserved in collisions — even in an inelastic crash where the objects crumple and stick (kinetic energy is lost to heat and sound, but momentum is not).
Friction opposes motion and turns useful energy into heat. Static friction (before something moves) is larger than kinetic friction (while it slides) — that's why it's harder to start pulling a heavy cart than to keep it moving. On a flat surface friction is proportional to the object's weight (its mass).
The six simple machines (lever, pulley, inclined plane, wedge, screw, wheel & axle) make work easier by trading force for distance. A gear is not one of the six. In a block-and-tackle pulley, the mechanical advantage equals the number of rope strands supporting the load — using more rope means you pull with less force.
A chemical change makes a brand-new substance through a reaction; a physical change only changes appearance, state, or motion — no new substance forms.
The steady back-and-forth swing of a pendulum is called simple harmonic motion (SHM). The time for one full swing (the period) is given by T = 2π√(L / g).
A swinging pendulum is also a great energy example: it's fastest (most KE) at the bottom and momentarily stops (most PE) at the ends of its swing.
This section digs deeper into forces — what they are, how they add up, how gravity works, and what happens in circles and collisions.
A force is a push or pull. To describe one fully you must give its size and direction (that's what makes it a vector). Force is measured in newtons and is tied to acceleration by F = m a — so force is never independent of acceleration.
When forces combine, the result depends on direction. Two forces of 14 and 2 add to anywhere between 12 (pointing opposite) and 16 (pointing the same way). When all forces cancel, the net force is zero and the object moves at constant velocity (or stays still) — this is balance, not an "unbalanced" force.
The gravitational pull between two objects depends on both of their masses and the distance between them. It follows an inverse-square law: F ∝ 1 / r². Double the distance → one-quarter the force; triple it → one-ninth.
On a planet with half of Earth's gravity, your weight is cut in half (980 N becomes 490 N) — but your mass stays the same. The universal gravitational constant G is identical everywhere in the universe, just very hard to measure precisely. Gravity reaches across empty space and theoretically acts over unlimited distance.
The normal force is the support push a surface gives, always perpendicular to that surface. On a flat floor it equals the object's weight; on a ramp it is less than the weight (only the part of weight pressing into the surface). Friction = (coefficient) × normal force, and in the standard model it is independent of contact area and of speed; the coefficient is a fixed property of the two surfaces.
To move in a circle, an object needs a force pulling it toward the center — the centripetal force. For a car rounding a curve, friction between the tires and road supplies it; for a planet, gravity does; for a rock on a string, tension does.
The "centrifugal" feeling of being flung outward isn't a real force — it's just your body's inertia wanting to keep going straight while the centripetal force curves your path.
In every collision, momentum is conserved. The difference is energy:
Archimedes' principle: the upward buoyant force on an object equals the weight of the fluid it pushes out of the way (displaces). Water pressure is greater at the bottom of a submerged object than the top, giving a net upward push.
Because a = F / m, you can change acceleration in predictable ways: increase mass and decrease force to guarantee less acceleration; do the opposite for more. A satellite's orbital speed depends on the central body's mass and the orbit's size — but not on the satellite's own mass.
At the deepest level, every interaction is one of four forces: gravity (weakest, holds planets in orbit), electromagnetism (holds atoms and tables together), the strong nuclear force (binds the nucleus), and the weak nuclear force (causes some radioactive decay). The first law of thermodynamics is really just conservation of energy.
This section is the calculation toolkit: kinematics equations, energy conservation, momentum, and how Newton's laws play out in real numbers.
When acceleration is steady, three equations solve almost everything. Starting from rest they simplify nicely:
Remember: a straight line on a position–time graph means constant velocity, so acceleration is zero. A glass you drop keeps speeding up because gravity accelerates it the whole way down.
Energy bookkeeping is often easier than tracking forces. As something falls, PE → KE; thrown upward, KE → PE. At the highest point of a throw, kinetic energy is lowest and potential energy is greatest.
Momentum p = mv is conserved in collisions. Impulse is the change in momentum, and equals force × time (J = F · t = Δp). Impulse and momentum share the units kg·m/s (= N·s).
An object in a circle has centripetal acceleration pointing to the center: a = v² / r. At the bottom of a curved track the acceleration points up (toward the center); at the top of a loop it points down. Angular momentum is the spinning version of momentum and is conserved for an isolated system.
Everything ties back to F = m a:
A force always pushes an object toward lower potential energy, and its strength is the negative slope of the PE graph: F = −(slope of U). If you know how potential energy U changes with position x, the force is how steeply U drops.
A point sitting at radius r on a spinning object travels in a circle. Its linear (straight-line) speed is the circumference times how many turns it makes each minute: v = 2πr × (turns per time).
Angular momentum is the spinning version of momentum: L = I × ω (moment of inertia × spin rate). Its units are kg·m²/s (compare to plain momentum's kg·m/s). The moment of inertia (I) measures how an object's mass is spread out from the spin axis — mass far from the center counts more.
This section covers fluids (pressure and floating), projectiles, and rotation — plus a few competition "odd unit" facts.
Pressure is force spread over an area: P = F / A, measured in pascals (Pa = N/m²). The same force on a smaller area makes a much higher pressure — which is why a ballerina on her tiptoes presses far harder on the floor than when standing flat.
Archimedes' principle says the upward buoyant force equals the weight of fluid displaced. An object floats if it is less dense than the fluid, sinks if denser, and stays suspended if equal. For something floating, the fraction of its volume underwater equals its density divided by the fluid's density.
A projectile's horizontal and vertical motions are independent. Gravity only affects the vertical part, so:
Torque is a twisting force = force × distance from the pivot (the "lever arm"). That's why doorknobs sit far from the hinges — a longer lever arm gives more turning effect for the same push. The net torque equals the rate of change of angular momentum.
On a rolling wheel, the top moves fastest relative to the ground (twice the bike's speed), while the contact point on the bottom is momentarily still. Rolling down a ramp, a solid sphere beats a cylinder, which beats a hoop — mass spread out on the rim (the hoop) slows it down.
Astronauts on the ISS feel weightless not because gravity is gone — Earth's gravity is still strong up there — but because they are in continuous free fall around Earth. Their mass and the force of gravity are unchanged; only their apparent weight is near zero.
One of the strangest ideas in physics: every moving object has a tiny "matter wave" with a wavelength given by λ = h / p, where h is Planck's constant and p is momentum. Because momentum is on the bottom, the wavelength is inversely proportional to momentum — heavier or faster objects have shorter wavelengths. To rank objects by increasing wavelength, rank them by decreasing momentum.
The center of mass is the average position of all the mass — the balance point. For objects along a line: CM = (m₁x₁ + m₂x₂ + …) ÷ (m₁ + m₂ + …).
Electrical energy used = power × time. A kilowatt-hour (kWh) is the energy of a 1000-watt device running for 1 hour — it's how electricity bills measure energy. Cost = energy (in kWh) × the price per kWh.
This section is all about work, energy, power, and the machines that put them to use — the heart of Test 3.
Work is the mechanical transfer of energy: W = F × d (force × distance moved in the force's direction). No movement means no work. Energy is the capacity to do work, and power is how fast work happens: P = W / t.
Energy constantly changes form but is never lost (conservation of energy):
Efficiency = useful work out ÷ total energy in (×100%). Because friction always wastes some energy as heat, the output is always less than the input, so a 100% efficient machine is impossible — that would violate the law of conservation of energy and the laws of thermodynamics. If output rises for the same input, efficiency went up.
Simple machines change the size or direction of a force, trading force for distance. The six are the lever, pulley, inclined plane (ramp), screw, wedge, and wheel & axle. A gear is not a simple machine, and a bicycle is a compound (complex) machine built from several. A chisel is a wedge; an ice-auger is a screw (an inclined plane wrapped around a cylinder; its "lead" is how far it advances per turn).
Mechanical advantage is how many times a machine multiplies your force. The Ideal MA (IMA) assumes no friction and comes from the machine's geometry:
The actual MA is always less than the IMA because of friction, and Efficiency = AMA ÷ IMA. To find effort: Effort = Load ÷ MA (a MA of 5 lifts a 10 N load with just 2 N).
Levers come in three classes by where the fulcrum, load, and effort sit:
A lever (or teeter-totter) balances when the torques match: m₁ × d₁ = m₂ × d₂.
This is the advanced/competition section: accelerating frames, electric and magnetic forces, heat engines, and tricky motion. These ideas power the hardest Bonus and Test 3 questions.
For an object hanging at rest, the string tension equals its weight (T = mg) — the upward pull balances gravity. But inside an accelerating elevator, your "apparent weight" changes:
The coefficient of friction is found from μ = friction force ÷ normal force, and on a level surface the normal force is mg. Watch your masses (and remember grams ↔ kilograms).
The latent heat of fusion is the energy needed to melt a unit mass of solid into liquid. During melting the temperature stays constant, because the energy is breaking molecular bonds rather than speeding particles up.
Some competition sets sneak in chemistry. Colligative properties depend only on the number of dissolved particles, not what they are. The classic pair is freezing-point depression and vapor-pressure lowering (density, color, and ionic strength are not colligative).
When a gas is squeezed or expands at steady pressure, the work done is W = P × ΔV (pressure × change in volume). This shows up in competition problems with odd units like "liter-atmospheres."
In electricity, energy = charge × voltage. That's why a volt times a coulomb gives a joule (energy), and why the tiny electron-volt is the energy one electron gains crossing a 1-volt difference. (Don't confuse it with the watt, which is power = energy per second.)
Click any card to expand. Every tip is pulled directly from the Chapter 4 practice and bonus question patterns.
The Study Guide tab now has six in-depth sections that together cover every question in this chapter. Here is the fastest path to a high score:
Across all 337 questions (285 practice + 52 bonus) and six study topics, these ideas appear again and again:
Each card shows what the formula means in plain English plus practice problems. Type an answer, then click Show Answer to check.
Essential definitions for Chapter 4. Use the highlighter toolbar to mark terms you need to review.
Click the ☆ star on any question in Practice Q&A or Bonus Challenges to save it here.