• The Bohr Model of the Hydrogen Atom

    Bohr postulated that the electron in the hydrogen atom could only exist stably in orbits that had angular momentum equal to an integer multiple of where called Planck's constant. Mathematically, for an assumed circular orbit, the angular momentum (1)...

    https://astarmathsandphysics.com/ib-physics-notes/the-history-and-development-of-physics/1326-the-bohr-model-of-the-hydrogen-atom.html
  • The Copenhagen Interpretation

    Quantum physics has as it's root that every particle may be described by a wavefunction. The wavefunction – which describes the motion of the particle – has no real physical interpretation. In general the wavefunction may take non real or imaginary...

    https://astarmathsandphysics.com/ib-physics-notes/the-history-and-development-of-physics/1327-the-copenhagen-interpretation.html
  • Symbols and Notation

    the set of positive integers and zero the set of integers the set of positive integers is less than is greater than is less than or equal to is greater than or equal to is not equal to the set of rational numbers the set of positive rational numbers...

    https://astarmathsandphysics.com/?id=1335:symbols-and-notation&catid=97
  • Finding the Intercept, Gradient and Area Under the Graph

    Three graphical concepts are very useful – the intercepts (particularly the y – intercept), the gradient of the graph at a point and the area under the graph. The intercept is a point on an axis where the graph crosses. If the graph is a line and the y...

    https://astarmathsandphysics.com/ib-physics-notes/measurements-units-uncertainty-and-principles/1341-finding-the-intercept-gradient-and-area-under-the-graph.html
  • Energy

    When work is done on an object, the object gains energy and the medium that does work loses energy. The amount of energy transferred is equal to the work done. It is not always equal to the amount of energy transferred to the object. Some energy is...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1362-energy.html
  • Energy of an Orbiting Satellite

    The gravitational potential energy of an orbiting satellite of mass m is given by (1) where is the mass of the Earth. We can find an expression for the kinetic energy by considering the equation for a satellite in a circular orbit. For such a...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1363-energy-of-an-orbiting-satellite.html
  • Free Body Diagrams

    A free body diagram illustrates all the forces acting on a particular object and leaves us in a position to apply Newtons second law – – easily. Often the forces will be balanced so the forces vertically and horizontal are equal, Generally this will...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1368-free-body-diagrams.html
  • Inertial Mass, Gravitational Mass and Weight

    We mislead ourselves when we say we are measuring the mass of an object. If fact we are measuring the force of gravity on that object and changing that force into a mass using a calibrated scale. If we were to 'measure' the mass of an object at...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1371-inertial-mass-gravitational-mass-and-weight.html
  • Bohr's Model of the Atom

    The evidence of energy levels in atoms is obvious from emission and absorption spectra. Each element has a set of frequencies of radiation which can be absorbed or emitted, corresponding to the energy levels between atoms. An atom is illustrated below....

    https://astarmathsandphysics.com/ib-physics-notes/quantum-and-nuclear-physics/1429-bohr-s-model-of-the-atom.html
  • The Stopping Potential

    When ligh is shone on a metal plate, photons are emitted – this is called the photoelectric effect. If the plate from which the electrons are emitted is at a potential difference relative to another plate, they will be accelerated if the second plate...

    https://astarmathsandphysics.com/ib-physics-notes/quantum-and-nuclear-physics/1436-the-stopping-potential.html
  • The Nature of Light

    Light is an electromagnetic wave. Physical waves – sound, waves on strings etc – involve the vibration of matter. Electromagnetic waves involve the vibration of magnetic fields and electric fields. They create each other – a changing electric field...

    https://astarmathsandphysics.com/ib-physics-notes/relativity/1453-the-nature-of-light.html
  • The Equation of State For an Ideal Gas

    The three gas laws that separately describe the behaviours of an ideal gas can be combined into a single equation called 'the equation of state'. These three laws, with =pressure (Pa or ), =Volume ( ) and =temperature (Kelvin or K), The Pressure Law, a...

    https://astarmathsandphysics.com/ib-physics-notes/thermal-physics/1481-the-equation-of-state-for-an-ideal-gas.html
  • Longitudinal Waves

    Longitudinal waves are waves such that the direction of travel of the wave, from left to right in the diagram below, is along the same line as the vibration of the wave, or the motion of the air molecules in the diagram below. Longitudinal waves are...

    https://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/1491-longitudinal-waves.html
  • Refraction of Waves

    If a wave is incident on the boundary between two media at an angle to the boundary, that part of the wave which is transmitted will change direction. It will be refracted. Any wave can be refracted – longitudinal (sound, pressure waves) or transverse...

    https://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/1494-refraction-of-waves.html
  • Standing Waves on Strings

    A standing wave occurs when a wave is confined in space. Repeated reflections occur from the walls of the space that confines the wave. For certain frequencies the time taken for a wave to travel back and force between the interval of confinement...

    https://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/1497-standing-waves-on-strings.html
  • Introduction to Angle Action Variables

    It is desirable to construct a coordinate system in which the Hamiltonian has the simplest possible form. In the case of rotational or librational motion one of those coordinates behaves like an angle and the conjugate variable is called the action –...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1524-introduction-to-angle-action-variables.html
  • Making Equations Dimentionless

    It is often useful to remove the units from an equation. We can see which physical mechanisms are more important and the equation to be solved is simpler. We scale all variables so that the variables become dimensionless. We can solve the equation...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1526-making-equations-dimentionless.html
  • The Hamiltonian

    The Hamiltonian represents the energy of the system which is the sum of kinetic and potential energy, labelled and respectively. For a one dimensional system, we may write so where Note that is a function of only and is a function of only. In general...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1537-the-hamiltonian.html
  • The Lagrangian Equation of Motion

    The Lagrangian is defined as where and is a function of Hence The first of Hamilton's equations gives so the bracketed term vanishes and leaves The other of Hamilton's equations is and we can use to give This is Lagrange's equation of motion. It is a...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1538-the-lagrangian-equation-of-motion.html
  • Alternative Forms of The Continuity Equation

    The continuity equation is usually written (1) where is the density of the fluid at a point. < > It may also be written (2) or (3) where is the Stokes derivative. < > (2) follows from (1) on using the identity < > To derive (3) write

    https://astarmathsandphysics.com/university-physics-notes/fluid-mechanics/1561-alternative-forms-of-the-continuity-equation.html

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