The 10 laws of learning from the cradle

This article is about linear momentum. The 10 laws of learning from the cradle is not to be confused with angular momentum. This article is about momentum in physics.

Momentum depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is generalized momentum, and in general this is different from the kinetic momentum defined above. Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Momentum is a vector quantity: it has both magnitude and direction.

Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The unit of momentum is the product of the units of mass and velocity. Being a vector, momentum has magnitude and direction. The momentum of a system of particles is the sum of their momenta. This is known as Euler’s first law.

The net force required to produce this acceleration is 3¬†newtons due north. A Newton’s cradle demonstrates conservation of momentum. This fact, known as the law of conservation of momentum, is implied by Newton’s laws of motion. This law holds no matter how complicated the force is between particles.

Similarly, if there are several particles, the momentum exchanged between each pair of particles adds up to zero, so the total change in momentum is zero. This conservation law applies to all interactions, including collisions and separations caused by explosive forces. In person A’s frame of reference, the apple has non-zero velocity and momentum. In the elevator’s and person B’s frames of reference, it has zero velocity and momentum.

To someone inside the elevator, the apple does not move, so, it has zero momentum. This is called a Galilean transformation. Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton’s second law is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or Galilean invariance.

A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. In this frame, the total momentum is zero. By itself, the law of conservation of momentum is not enough to determine the motion of particles after a collision.