Introduction In this short article, I’ll give a geometric motivation for the definition of the inner product of vectors ( also called scalar product). The objects that we will be considering are arrows in the three-dimensional space and they will be represented by Latin letters with an arrow above them like , or . The
The moment of inertia of a rigid body is clearly defined and explicit calculations for a thin rod or stick, a cylindrical shell and a disk, are made.
The one-dimensional simple harmonic oscillator is described by the differential equation (1) Here is the mass of the particle and is the constant characterizing the restoring force. Solution of the simple harmonic oscillator The solution satisfying the initial condition , where is the amplitude of the oscillations, is given by (2) The oscillator