Note: All quantities in bold represent vectors.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects.[1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known.[2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of reference. The point of concurrency of the three axes is known as the origin of the particular space.[3]
Classical mechanics utilises many equationsāas well as other mathematical conceptsāwhich relate various physical quantities to one another. These include differential equations, manifolds, Lie groups, and ergodic theory.[4] This page gives a summary of the most important of these.
Contents[hide] |
Name of equation | Equation | Year derived[5] | Derived by | Notes |
---|---|---|---|---|
Center of mass | Discrete case:
where n is the number of mass particles. Continuous case: where Ļ(s) is the scalar mass density as a function of the position vector |
1687 | Isaac Newton |
average velocity = change in distance / change in time.
(R = radius of the circle, Ļ = v/R angular velocity)
For a single axis of rotation: The moment of inertia for an object is the sum of the products of the mass element and the square of their distances from the axis of rotation:
Vector form:
(Note: I can be treated like a vector if it is diagonalized first, but it is actually a 3Ć3 matrix - a tensor of rank-2)
r is the radius vector.
if |r| and the sine of the angle between r and p remains constant.
This one is very limited, more added later. Ī± = dĻ/dt
Omega is called the precession angular speed, and is defined:
(Note: w is the weight of the spinning flywheel)
for m as a constant:
These equations can be used only when acceleration is constant. If acceleration is not constant then calculus must be used.
These equations can be adapted for angular motion, where angular acceleration is constant: