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Physics

Exercises in C++

Physics: 0% done

Module 1 · Measuring the world: units, sizes and estimates

Physics looks for the few rules behind everything

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1 / 232 · Measuring the world: units, sizes and estimates

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, 1 to practisePhysics looks for the few rules behind everything
The C++ this course computes with
, 1 to practiseSeven base units measure everything
, 1 to practisePowers of ten and prefixes
, 2 to practiseConvert units by multiplying by one
, 2 to practiseDimensional analysis checks a formula before you trust it
, 1 to practiseSignificant figures say how precise a number is
, 2 to practiseEvery measurement comes with an uncertainty
, 1 to practiseFermi estimates get within a factor of ten in a minute
, 1 to practiseFrom protons to the observable universe
, 4 to practisePractice problems
Recap

, 1 to practisePosition is measured from an origin you choose
, 1 to practiseSpeed has no direction; velocity does
, 1 to practiseOn a position–time graph, the slope is the velocity
Instantaneous velocity is the slope of the tangent
, 2 to practiseAcceleration is how fast the velocity changes
, 1 to practiseOn a velocity–time graph, the area is the displacement
, 2 to practiseFour equations for constant acceleration
, 1 to practiseStopping distance grows with the square of speed
, 1 to practiseFree fall is constant acceleration downward
, 2 to practiseStep motion through time, the way simulations do
, 4 to practisePractice problems
Recap

, 1 to practiseA vector is a size and a direction
, 1 to practiseBreak a vector into components
, 2 to practiseAdd vectors tip to tail, or by components
, 1 to practiseVelocity depends on who is watching
, 1 to practiseA projectile is two motions at once
The flight of a thrown ball is a parabola
, 1 to practiseForty-five degrees goes farthest
, 2 to practiseSimulate a projectile step by step
, 2 to practiseMoving in a circle means accelerating towards the centre
, 4 to practisePractice problems
Recap

, 1 to practiseA force is a push or a pull
, 1 to practiseWith no net force, motion does not change
, 1 to practiseForces add as vectors into one net force
, 2 to practiseThe second law: force equals mass times acceleration
, 1 to practiseMass is how much stuff; weight is gravity’s pull on it
, 1 to practiseFree-body diagrams show every force on one object
, 2 to practiseThe normal force is whatever stops you going through the floor
, 1 to practiseTension pulls along a rope
, 1 to practiseForces come in pairs on different objects
, 1 to practiseEquilibrium: when the forces balance
, 4 to practisePractice problems
Recap

, 1 to practiseFriction holds until it can’t, then slides
, 2 to practisePushing a box: friction in the second law
, 2 to practiseOn a slope, split gravity along and across it
, 1 to practiseTilt until it slips to measure friction
, 1 to practiseAn Atwood machine: two masses and a pulley
, 1 to practiseHooke’s law: a spring pulls back in proportion
, 1 to practiseDrag grows with speed until it balances weight
, 1 to practiseSimulate a fall with drag
, 1 to practiseSomething must supply the centripetal force
, 1 to practiseGoing over the top of a loop
, 4 to practisePractice problems
, 2 to practiseMore practice: drag and loops
Recap

, 1 to practiseEnergy is never made or destroyed, only moved
, 2 to practiseWork is force times distance along the force
When the force changes, work is the area under F against x
, 2 to practiseKinetic energy, and the work–energy theorem
, 1 to practisePotential energy is stored work
, 1 to practiseWithout friction, kinetic plus potential stays constant
, 1 to practiseEnergy ignores the shape of the path
, 1 to practiseFriction turns mechanical energy into heat
, 2 to practisePower is how fast energy is moved
, 1 to practiseEfficiency: how much of the energy does the job
, 4 to practisePractice problems
Recap

, 1 to practiseMomentum is mass times velocity
, 2 to practiseImpulse: a force over time changes momentum
, 2 to practiseIn an isolated system, total momentum never changes
, 1 to practiseObjects that stick together lose kinetic energy
, 1 to practiseElastic collisions keep the kinetic energy too
, 1 to practiseElastic, inelastic, perfectly inelastic
, 1 to practiseIn two dimensions, each component is conserved
, 1 to practiseThe centre of mass moves as if all the mass were there
, 2 to practiseA rocket pushes itself by throwing mass backwards
, 4 to practisePractice problems
Recap

, 1 to practiseAngles, angular velocity and angular acceleration
, 1 to practiseThe equations of motion, for spinning
, 1 to practiseRolling without slipping: the bottom is still
, 2 to practiseTorque is the turning effect of a force
, 2 to practiseMoment of inertia: mass, and where it sits
, 1 to practiseA rolling object has two kinds of kinetic energy
, 1 to practiseTry it: the speed of a rolling object
, 1 to practiseAngular momentum is conserved: spin faster by pulling in
, 1 to practiseBalance needs zero net force and zero net torque
, 1 to practiseA spinning top turns sideways instead of falling
, 4 to practisePractice problems
Recap

, 1 to practiseEvery mass attracts every other mass
, 2 to practiseLittle g comes from big G
A gravitational field fills the space around a mass
, 2 to practiseAn orbit is falling and always missing
Kepler’s laws: ellipses and equal areas
, 1 to practiseFarther planets take much longer
, 1 to practiseGravitational energy is negative, and escape means reaching zero
, 1 to practiseTry it: escape velocity
, 1 to practiseGeostationary orbit: one turn a day
, 1 to practiseTides come from the difference in the Moon’s pull
, 1 to practiseSimulate an orbit step by step
, 4 to practisePractice problems
Recap

, 1 to practisePeriodic motion repeats itself
Simple harmonic motion: the restoring force is proportional to displacement
, 1 to practiseFastest in the middle, hardest pulled at the ends
, 3 to practiseA mass on a spring: stiffer is faster, heavier is slower
, 2 to practiseA pendulum keeps time with its length
, 1 to practiseBig swings take longer
, 1 to practiseEnergy sloshes between kinetic and potential
, 1 to practiseDamping makes oscillations die away
, 2 to practiseSimulate a damped spring
, 1 to practiseResonance: push at the natural frequency
, 4 to practisePractice problems
Recap

, 1 to practiseA wave carries energy, not matter
, 2 to practiseSpeed is wavelength times frequency
, 2 to practiseThe medium sets the speed
Waves add up where they meet
, 2 to practisePath difference decides loud and quiet
, 1 to practiseStanding waves fit a whole number of halves
, 1 to practiseHarmonics give an instrument its voice
, 1 to practiseSound is a pressure wave
, 1 to practiseLoudness is counted in decibels
, 1 to practiseA moving source changes the pitch
, 4 to practisePractice problems
Recap: waves and sound

, 1 to practiseA fluid flows, and density says how heavy it is
, 1 to practisePressure is force spread over area
, 2 to practisePressure grows with depth
, 1 to practiseA push on a fluid reaches everywhere
, 2 to practiseArchimedes: the push up equals the fluid pushed aside
, 1 to practiseWeighing something under water
, 1 to practiseNarrower pipe, faster flow
, 2 to practiseBernoulli: faster flow, lower pressure
, 1 to practiseViscosity is a fluid’s internal friction
, 3 to practisePractice problems
Recap: fluids

, 1 to practiseTemperature measures jiggling, and has a true zero
, 1 to practiseMost things grow when they warm up
, 2 to practiseHeat is energy on the move
, 2 to practiseMelting and boiling take heat without warming
, 1 to practiseHeat moves by conduction, convection and radiation
, 1 to practiseThe ideal gas law ties pressure, volume and temperature
, 1 to practisePressure is molecules hitting the walls
, 2 to practiseThe first law: energy is conserved
, 1 to practiseA heat engine can never use all its heat
, 1 to practiseEntropy never goes down
, 4 to practisePractice problems
Recap: heat and thermodynamics

, 1 to practiseCharge comes in two kinds and in fixed lumps
, 1 to practiseConductors let charge move; insulators hold it
, 2 to practiseCoulomb's law: an inverse square
, 2 to practiseA charge fills the space around it with a field
, 1 to practiseField lines draw the field
, 2 to practiseVoltage is energy per charge
, 1 to practiseThe field points downhill in potential
, 2 to practiseA capacitor stores charge, and energy
, 1 to practiseGauss's law: count the field lines leaving
, 3 to practisePractice problems
Recap: charge and fields

, 1 to practiseCurrent is charge flowing per second
A circuit is a closed loop
, 2 to practiseResistance and Ohm's law
, 2 to practisePower is voltage times current
, 1 to practiseSeries adds resistance; parallel adds paths
, 2 to practiseKirchhoff's laws solve any circuit
, 2 to practiseA capacitor charges along an exponential
, 1 to practiseMains electricity, and staying safe
, 3 to practisePractice problems
Recap: current and circuits

, 1 to practiseMagnets have poles and fill space with a field
, 2 to practiseA magnetic field pushes moving charges sideways
, 1 to practiseA current in a field feels a force: the motor
, 2 to practiseCurrents make magnetic fields
, 2 to practiseFaraday: changing flux makes a voltage
, 1 to practiseLenz's law: induction opposes the change
, 1 to practiseA generator spins a coil in a field
, 1 to practiseTransformers change voltage, and save power on the grid
, 1 to practiseMaxwell's equations unite electricity, magnetism and light
, 4 to practisePractice problems
Recap: magnetism and induction

, 1 to practiseLight is one band of the electromagnetic spectrum
, 2 to practiseLight is fastest in a vacuum
, 1 to practiseReflection: the angles are equal
, 2 to practiseRefraction and Snell's law
, 1 to practiseTotal internal reflection traps light
, 2 to practiseLenses form images: the thin lens equation
, 2 to practiseTwo slits prove light is a wave
, 1 to practisePolarisation shows light is transverse
, 4 to practisePractice problems
Recap: light and optics

Two postulates, and the speed of light is the same for everyone
, 1 to practiseSimultaneous for you is not simultaneous for me
, 2 to practiseThe Lorentz factor measures how relativistic you are
, 2 to practiseMoving clocks run slow
, 2 to practiseMoving lengths shrink, along the motion
, 2 to practiseSpeeds add in a way that never passes c
, 1 to practiseSpacetime diagrams draw time and space together
, 1 to practiseMass is a form of energy
, 1 to practiseA glimpse of general relativity: gravity is curved spacetime
, 3 to practisePractice problems
Recap: special relativity

, 2 to practiseHot things glow, and classical physics got it wrong
, 2 to practiseThe photoelectric effect: light comes in photons
, 2 to practiseA photon carries energy and momentum
, 2 to practiseEverything is both wave and particle
, 1 to practiseYou can’t know position and momentum exactly at once
, 1 to practiseAtoms have energy levels, and spectra are their fingerprints
, 1 to practiseThe wavefunction gives probabilities
, 1 to practiseParticles tunnel through walls
, 1 to practiseThe nucleus, and radioactive decay
, 4 to practisePractice problems
Recap: quantum physics

, 2 to practiseHow an expert attacks a problem
, 1 to practiseSimulating motion: not all steps are equal
, 1 to practiseWrite a Verlet stepper
, 1 to practiseRunge–Kutta: sample the slope four times
, 1 to practiseThe Lagrangian: physics from one function
, 1 to practiseNoether: every symmetry gives a conservation law
, 2 to practiseChaos: simple rules, unpredictable motion
, 1 to practiseThe Standard Model: what everything is made of
, 1 to practiseWhat physics doesn’t know yet
, 4 to practiseMastery questions: everything at once
, 3 to practisePractice problems: motion and energy
, 3 to practisePractice problems: heat, fields and light
Recap: physics like an expert