• Table of Normalized Spherical Harmonics

    The Schrodinger equation for the hydrogen atom takes the form This equation is separable which means that while the solution is a function of three variables, it is a product of three functions, each one of which is a function of only one variable, The...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1643-table-of-normalized-spherical-harmonics.html

  • Table of the Radial Parts of the Wavefunctions for the Hydrogen Atom

    The Schrodinger equation for the hydogen atom takes the form This equation is separable which means that while the solution is a function of three variables, it is a product of three functions, each one of which is a function of only one variable, The...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1644-table-of-the-radial-parts-of-the-wavefunctions-for-the-hydrogen-atom.html

  • The Simple Harmonic Oscillator

    The simple harmonic oscillator models the motion of a wavefunction subject to the potential function illustrated below. The Schrodinger equation becomes The first few solutions, in order of increasing energy, are shown below. In this table and Quantum...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1655-the-simple-harmonic-oscillator.html

  • Analysis of a Plane Blown Off Course

    Suppose a plane can fly 300km/h in still air. It wishes to fly from a town A to a town B on a bearing of 030 o to a town B. The wind is blowing at 20km/h on a bearing of 300 o . If the pilot aims the plane on to fly to B, he will be blow off course by...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/5031-analysis-of-a-plane-blown-off-course.html

  • Proof That Polar Moment of inertia Equals Sum of Moments of Inertia Aboput x and y Axes

    The polar moment of inertia of a lamina with surface \[S\] about a axis through the origin perpendicular to the \[xy\] plane is given by \[I_P \int_S r^2 \rho (x,y) ddS\] where \[r^2 =x^2 +y^2 \] The moment of inerta of the lamina about the \[x\] and...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/3971-proof-that-polar-moment-of-inertia-equals-sum-of-moments-of-inertia-aboput-x-and-y-axes.html

  • Moment of Inertia of a Cube About an Edge

    Supppse a cube of side \[a\] of variable density \[\rho = k(x+y+z)\] with one vertex at the origin at edges parallel to the axes is allowed to rotate about an axis. What is the moment of inertia of the cube about that axis? A volume element...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5371-moment-of-inertia-of-a-cube-about-an-edge.html

  • Motion in a Circle With Non Constant Acceleration

    Suppose a particle is moving on a circle of radius \[r\] with at any time \[t\] the ant clockwise angle of the particle from the positive \[x\] axis being given by \[\theta = \frac{t}{t+1}\] /> br /> the angular velocity is \[\omega = \frac{d \theta...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5378-motion-in-a-circle-with-non-constant-acceleration.html

  • Motion Defined Parametrically With Non Constant Acceleration

    Suppose a a particle is moving along a curve with Cartesian coordinates given parametrically in terms of time \[t\] by \[x=\sqrt{t^2+1}, \; y= \sqrt{2t}\] then the distance of the particle from the origin is \[r= \sqrt{x^2+y^2}= \sqrt{t^2+1+2t}=t+1\]....

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5379-motion-defined-parametrically-with-non-constant-acceleration.html

  • Angular Velocity and Acceleration Along Curve

    Suppose a particle moves along the curve \[y^2=x^3\] . If the horizontal velocity is constant and equal to 2 units/s, find the angular velocity \[\omega\] and the angular acceleration \[\alpha\] . The particle is at a point \[\theta = tan^{-1}...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5380-angular-velocity-and-acceleration-along-curve.html

  • Velocity and Acceleration of Piston Operated By a Flywheel

    A piston moved by a rod fixed to the edge of a rotating flywheel will move backwards and forwards as the wheel rotates. If the radius of the flywheel is \[R\] and the length of the rod is \[l\] . and we let the centre of the flywheel be the origin, then...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5386-velocity-and-acceleration-of-piston-operated-by-a-flywheel.html

  • Proof of Stefan Boltzmann Law

    According to Planck's radiation law, the radiation density is \[I= \frac{2 h}{c^2} \int^{\infty}_0 \frac{f^3}{e^{\frac{hf}{kT}} -1} df=\frac{2 h}{c^2} \int^{\infty}_0 \frac{f^3}{1-e^{- \frac{hf}{kT}}} e^{-\frac{hf}{kT}} df\] . Substitute \[\frac{hf}{kT}...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/5401-proof-of-stefan-boltzmann-law.html

  • The Catenary

    Suppose a length \[L\] of chain is hung from an uneven ceiling. The ends of the chain are fixed to two points some distance apart. What will be the shape of the chain? Let the chain lie in the vertical \[xy\] plane. An small length \[ds\] of chain of...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5425-the-catenary.html

  • Particle Moving Along y Axis on Surface of Rotating Ellipse

    Suppose an ellipse with one focus at the origin is made to rotate about the origin in the \[xy\] plane. A particle on the surface of the ellipse is made to move on the surface of the ellipse as the ellipse rotates. What will be the velocity and...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5387-particle-moving-along-y-axis-on-surface-of-rotating-ellipse.html

  • Quantum Physics and Pure Numbers

    significant figures.. In the case of numbers this is true even for those numbers like \[e\] , and in the case of quantum mechanics, even for those quantities that are the exact solutions too some exact equation, like the metafunction of an electron...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5449-quantum-physics-and-pure-numbers.html

  • The Old Style Cathode Ray Tube

    The cathode ray tube is a very common device used in television sets and computer screens. Inside the tube is a vacuum, so the electrons are free to move and do not hit any gas molecules. Electrons are emitted from a negative cathode at A, which is...

    https://astarmathsandphysics.com/gcse-physics-notes/834-the-old-style-cathode-ray-tube.html

  • University Maths and Physics Tuition

    Level: Fluid Dynamics Approximation Theory Topology Differential Geometry Calculus Statistics Electromagnetism Quantum Mechanics Non Linear Dynamics Mechanics Group Theory Optics Galois Theory Physical Chemistry Abstract Algebra Number Theory Planetary...

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  • Degree Level Physics Tuition Throughout London By Physics Specialists

    be asked. We Tutor These Physics Topics Up To Degree Level - And Have Written Our Own Course Notes Astronomy Classical Mechanics Electricity and Magnetism Experimental Physics Fluid Mechanics Light and Optics Non Linear Dynamics Physical Chemistry...

    https://astarmathsandphysics.com/physics/degree-level-tuition.html

  • Postulates of Relativity

    Newtonian mechanics is based on two principles: Space and time are absolute. The time coordinates given to observations in all inertial frames are related by a constant time shift. In particular, all observers in all inertial frames agree on the time...

    https://astarmathsandphysics.com/ib-physics-notes/relativity/1442-postulates-of-relativity.html

  • The Relationship Between Spin, Orbital and Total Angular Momentum

    For an atom in groups 1 or 2, or periods, 2 or 3 of the periodic table, any electron with spin oriented up will be opposed by an electron in the same otherwise identical set of quantum numbers with opposing spin, and any electron with values of angular...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/5454-the-relationship-between-spin-orbital-and-total-angular-momentum.html

  • Sankey Diagrams

    Sankey diagrams show what happens to the energy used during a chemical or physical process. The amount of energy input or used up beach part of the process is represented by a bar with an arrow indicated the direction of the process, with the thickness...

    https://astarmathsandphysics.com/gcse-physics-notes/812-sankey-diagrams.html

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