Skill — Solve symbolically before substituting numerical values.
Appears in chapters
02·03·07
Linked atoms
158 linked atoms.
01 Kinematics
02 Forces and Newton’s laws
03 Inclined plane and circular motion
- Centripetal acceleration of Earth’s rotation
- Flat curve, dry and wet
- Derivation of centripetal acceleration
- The conical pendulum
- The Atwood pulley: the force on the axle
- The accelerating matchbox
- Spring in rotation
- Problem — Ball on a rotating spring
- Pulley on a double inclined plane
- Problem — Four linked discs
- Problem — Ranking points on a rotating disc
- Problem — Ranking four circular motions
- Problem — Maximum velocity on a flat curve
04 Energy and work
- Definition and formula of work
- Worked example — minimum height for the loop
- Problem — Water and oil at different temperatures
- Problem — Block on an inclined plane with a spring (equilibrium and oscillations)
- Problem — From kinetic energy to velocity
- Problem — Two springs and a box
- Problem — Kinetic energy of a ball
- h
- Problem — Kinetic energy and doubled velocity
- Problem — Work done by an inclined force
- Problem — Work and direction: the suitcase
- Problem — Power of a lift
- Problem — Volcanic rock in the Fanta
- Problem — Bungee jump
- Problem — Lifting and lowering a book
- Problem — Change in potential energy of a box
- When work is zero
04b Oscillations and simple harmonic motion
- Worked example — Finding A and φ from initial conditions
- The equation of simple harmonic motion
- Normal modes of the coupled oscillator
- Problem — Mass between two springs, equivalent K
- Problem — Mass on two springs in parallel
05 Momentum and collisions
- Life-saving shock absorbers
- Problem — Car versus lorry
- Problem — Bowling ball versus pin
- Problem — Crash test with airbag
- Problem — Derivation of the 1D elastic collision
- Elastic tennis
- Worked example — 1D elastic collision
- Newton’s cradle
- The ball that comes back
- Problem — Momentum of a car
- Sudden swerve (impulse)
- Elastic collision in 1D
- Velocity from the total momentum
06 Centre of mass
- Derivation of König’s theorem
- Derivation of König’s theorem
- Finding the masses from the centre of mass
07 Rotational dynamics
- Problem — Atwood machine with a massive pulley
- Problem — Pulley with two radii
- Pulley with two radii
- Newton’s second law for rotation
08 Universal gravitation
- Altitude of a geostationary orbit
- Derivation of escape velocity
- Binding energy of a satellite
- Worked example: the mass of the Sun from Kepler’s law
- Gravitational force Sun-Earth
- Gravitational force Earth-Moon
- Force between two 100 kg spheres
- Gravity on the Moon and an astronaut’s weight
- Surface gravity on the Moon
- Surface gravity on the Moon
- Newton’s law of universal gravitation
- The hollow Moon
- Mass of an unknown planet
- Apple and Earth: mutual gravitational forces
- Circular orbit and centripetal force
- Period of a planet at 2.4 AU
- Period of a satellite at 400 km
- Weight and mass
- Planet from Kepler — mass of the star, velocity and energy
- Matching with mgh near the surface
- Radius of the geostationary orbit
- Radius of a planet
- Ranking the periods of four satellites
- Ranking the surface gravity of three planets
- s²
- Estimating the radius of the geostationary orbit
- Estimating the mass of the Galaxy
- Hohmann transfer Earth-Mars
- Escape velocity from Earth
09 Kinetic theory of gases
- Problem — Derivation of PV = nRT
- Problem — Drill on the v_rms of nitrogen
- Problem — Hydrogen or oxygen faster
- Problem — Pressure of an ideal gas
- Problem — Critical temperature from Van der Waals
- Problem — Temperature from v_rms
- Problem — Escape temperature of hydrogen
- Problem — Root-mean-square velocity of nitrogen
- Problem — Root-mean-square velocity and the speed of sound
10 Irreversible transformations and energy balance
- Inverse: from W to the ratio of volumes
- Heating at constant pressure: the coefficient Cp
- Challenge: mercury barometer
12 Cycles and heat engines
- Problem — Carnot compared with other cycles
- Problem — Adiabatic compression of a diatomic gas
- Problem — Derivation of Carnot efficiency
- Problem — Fridge as a reverse cycle
- Problem — Useful work for 1000 J absorbed
- Problem — Why engines run at high temperature
- Problem — Ideal heat pump for a house
- Problem — Heat pump for heating (295-273 K)
- Problem — Heat pump between 295 and 246 K
- Problem — Maximum Carnot efficiency (500-300 K)
- Problem — Minimum temperature of a power plant
13 Coulomb force and electrostatics
- Electrostatic equilibrium
- Worked example — Charge on a spring, equilibrium and expansion
- Problem — Given E, find r
- Problem — Given F, find q
- Problem — Equilibrium of three charges on an axis
- Problem — Equilibrium on a straight line
- Problem — Challenge: equilibrium of three aligned charges
15 Electric circuits
- Worked example — infinite ladder (R_A=1, R_B=3)
- Worked example — infinite ladder (R_A=2, R_B=4)
- The self-similarity trick
- Problem — resistance of an infinite ladder
18 Electromagnetic induction
19 Maxwell’s equations and electromagnetic waves
20 Special relativity
- From the gamma factor to velocity (proton)
- From the Doppler ratio to velocity
- Worked example — The Higgs boson at 0.8c
- Mr Rossi goes to the theatre
- The traveller at the cinema
- Invariant mass of two photons
- Problem — Velocity composition via Doppler
- Problem — Contraction of a rod
- Problem — Contraction of a spaceship
- Problem — Derivation of the energy-momentum invariant
- Problem — Rest energy of the electron
- Problem — Lorentz factor at 0.6c
- Problem — Lorentz factor of the muon
- Problem — GPS, quantitatively
- Problem — Spacecraft and the beeps
- Problem — Particle or photon
- Problem — Redshift of a galaxy
- Problem — Gravitational redshift on Everest
- Problem — Ruler moving at 0.6c
- Problem — A red traffic light seen as green
- A relativistic timer
- Velocity for gamma equal to 2
21 Introduction to quantum mechanics
- Derive the radius of the Bohr orbit
- Problem — Spectral width and mean lifetime
- Problem — Infinite potential well
- Problem — Black body at different temperatures
- Problem — Current from an illuminated semiconductor
- Problem — From lambda to the initial level (Balmer)
- Problem — de Broglie wavelength of an electron at 100 V
- Problem — Sci-fi physics, reducing h and the atomic volume
- Problem — Uncertainty of the electron in an atom
- Problem — Polariser and photon counting
- Problem — X-rays from ionised fluorine
- Problem — Deriving h from photoelectric data
- Problem — Stellar spectrum and the 397 nm line