You can use a spherical blackboard for many things, including the teaching of geographical coordinates, as a model for a closed Universe, or simply as a mathematical shape.
In the non-Euclidean geometry of the sphere, a circle will have a circumference greater than 2πr and an area greater than πr2. A triangle’s angles will add to more than 180°, and two parallel lines, called Great Circles, will converge.
A Universe with a density parameter Ω greater than unity will have too much mass to overcome its own gravitational...
Total internal refraction of laser beam through sugar solution with refractive index gradient; representative of seismic waves through Earth's mantle.
What it shows:
As a simulation of atmospheric refraction, this demonstration shows the gradual and continuous bending of light due to a gradient in the optical density of the medium. In this case the variable refracting medium is a tank of sugar water with a vertical gradient in the concentration of sugar and a HeNe laser provides the light beam. It can be used as a model of mirage formation (except that the...
For a body to reach terminal velocity when falling through a fluid, the drag force (given by Stoke's Law) coupled with the buoyant force (from Archimedes' principle) need to balance the falling object's weight. Leaving derivations to other great texts you end up with
Vector representation of position, velocity, and acceleration.
What it shows:
A circular train track1 is mounted on a board. X-Y axes are painted on the board with the origin at the center of the circle. Vector Arrows (Newtonian Mechanics, Vectors and Forces in Equilibrium) representing position, velocity, or acceleration may be attached to the train to...
The instructor breaks several boards with a swift blow of the hand.
What it shows:
The impulse momentum theorem is demonstrated in a most dramatic way by breaking several boards with the blow of your fist. You need not be a karate expert to show how the force of a well executed hammer-fist strike will easily break a stack of five to eight boards. The impulse is given by
impulse = F∆t = ∆mv
The point of the demonstration is: the greater the speed, the smaller ∆t will be and thus the greater the force.
A simple and convincing demonstration of the intermediate axis theorem. Consider an object (a tennis racquet in this case) with three unequal principle moments of inertia. If the racquet is set into rotation about either the axis of greatest moment or least moment and is thereafter subject to no external torques, the resulting motion is stable. However, rotation about the axis of intermediate principle moment of inertia is unstable — the smallest perturbation grows and the rotation axis does not remain close to the initial axis of rotation.
In explaining the electron orbits in the Bohr atom, de Broglie's principle of particle wave duality allows you to treat the electrons as waves of wavelength nλ = 2πr where r is the radius of the orbit. Then the only orbits allowed are those which are integer...