This scalar valued function \(V(\vec{r})\) is called the potential energy, or the potential for short. It has a direct connection to work and kinetic energy (which are also scalars of course):

The potential energy, PE, of a system is the energy it possess by virtue of its position within a gravitational field, or less formally its height. If a particle of mass \(m\) is raised by some height \(h\) then the work done in moving the particle is equal to

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum.

2019年2月19日 · One way is by defining momentum. This allows us to see a force acting on an object for a certain amount of time adding something to the object that represents its motion (the momentum). The amount of momentum a force adds to an object equals the force times the time it acts (or, better, the integral of the force over the time).

In lecture L9, we saw the principle of impulse and momentum applied to particle motion. This principle was of particular importance when the applied forces were functions of time and when interactions between particles occurred over very short times, such as with impact forces.

The interatomic forces can be estimated by doing quantum-mechanical calculations, and the results can be approximated by a suitable potential energy function. Here are a few examples showing how you can integrate forces to calculate potential energy

2016年12月25日 · The impulse-momentum theorem for rotational motion relates applied torque and change in angular momentum. If a torque with magnitude M is applied to a rotating body in the time interval between t 1 and t 2 so that the angular momentum of the body is changed from L 1 to L 2, then the impulse-momentum theorem for rotational motion states that:

Through this equation, it was proved that there are in nitely many energy angular momentum de-pendent potentials V (r; E; L) that lead to closed orbits. The study was done by generalizing the well known substitution r = 1=u in Newton's orbit equation to the substitution r = 1=s(u; E; L) in the equation of motion.

We explain the work-energy theorem and solve an example problem involving the equations for work and kinetic energy. We also discuss when work has a positive or negative value. We investigate Hooke's Law as we explore the concept of spring potential energy. We also examine how to find this energy mathematically and graphically.

We can determine how high on the ramp the two-block combination will go (in either direction) by using mechanical energy conservation. At the moment of the collision, all of the double-block's energy is kinetic, and when it stops on the ramp, it is all potential, so conservation demands: