What's the difference between momentum and kinetic energy?

Question

What are they measuring?

Answer 1

The formulas for momentum and kinetic energy are

p = mv
E = 1/2 m v^2

Technically speaking, if we were willing to do enormously more cumbersome mathematics, we don't need to use the concept of energy in Newtonian mechanics. If we assume that momentum is conserved, and that the motion of the center of mass of any system is constant, caculations can be carried out without resorting to the "law of conservation of energy". However, it works out that if we assume that the term 1/2 m v^2 is conserved, then we can dispense with the bother of calculating the center of mass of the entire system, before and after any collisions or interactions.

Energy is a concept that came in after Newton published his Principia, even though Work, which is dimensionally the same as Energy, was described in his time, Work being Force times Distance. It's helpful to remember the following relations, in understanding the distinction between momentum and energy:

p = Momentum = Force x Time = F*t
E = Energy = Force x Distance = F*d

So, for example, when a pitcher throws a fastball, if he exerts a force F on the baseball during his throw, then the baseball's

Momemtum would be F x (duration of his throw) = F*t
Energy would be F x (length of his throw) = F*d

Conservation of momentum is the consequence of physical laws being invariant with respect to translations in space (spatial symmetry), while conservation of energy is the consequence of physical laws being invariant with respect to shifts in time (temporal symmetry), as per Noether's Theorem.
In Hamiltonian and Quantum physics, p and x are conjugate variables, while E and t are also conjugate variables. It is impossible by the Heisenburg uncertainity principle that one can know a particle's momentum and position both as precisely as one wants, nor one can know a particle's energy and time of measurement both as precisely as one wants. But it's quite possible to know a particle's momentum and energy as precisely as you want at the same time, you just then can't know precisely when or where it was measured!

Answer 2

A couple things are important. One, momentum has a direction. Kinetic energy does not. Kinetic energy can be conserved by things flying off in any direction - forward, back the way they came, up, down, or sideways. For momentum to be conserved, some motion has to be conserved in the same direction, although new motion can start as long it is compensated by an equal amount of momentum in the opposite direction. The other thing I don't know how to say without being a little bit mathematical. Momentum is related to a force acting over time. Kinetic energy is related to a force acting over distance. Of course, every force acts over some amount of time, however small, and some amount of distance, however small.

Answer 3

In strictly abstract terms,

momentum = p = mv

kinetic energy = T = (1/2)mv^2

where m is the mass of the system under consideration and v is the velocity of the system.

For one thing, they have different dependences on velocity : momentum has a linear dependence and kinetic energy a quadratic dependence.

In physical terms, momentum is a distinct physical quantity, & isn't a measure of something else. Kinetic energy is the component of the total energy of the system that goes into causing the system to move.

When you move into relativistic & quantum physics, the distinctions become sharpened. For example, the energy of a quantum system can always be determined by its wave equation. The momentum of the system, on the other hand, cannot be determined precisely. It is subject to the uncertainty principle and thus cannot be determined to arbitrary accuracy.

Answer 4

P = mv; where P is momentum, m is mass, and v is the velocity of the mass.

KE = 1/2 mv^2; where KE is kinetic energy for the same m and v as in P.

If you want to break out KE, you can write 1/2 mv v = 1/2 Pv. This shows how momentum and KE are related. That is, momentum is one of the factors in the KE equation.

Momentum is measuring the resistance to change in velocity. It is this resistance to change that Newton is talking about in his first law. The change in momentum over time dP/dt = d(mv)/dt = m dv/dt (when mass is a constant) = ma because dv/dt = a = acceleration. In other words, force is required to change momentum.

Kinetic Energy is the capability to move things or cause a change. When moving a mass (m), which takes work, we create kinetic energy W = KE = Fd; where W is work and d is the distance a mass is moved by the force F. Thus KE = 1/2 mv^2 = Fd = mad Or, KE/F = d, which means it takes KE using a force F to move a mass d distance. Thus, in this case, KE is used to move things.

As we might guess, since one is a factor of the other, both P and KE have their conservation laws. The conservation of momentum and the conservation of energy laws are frequently invoked to solve physics problems.

Answer 5

Momentum P of a body of mass m and moving
with velocity v is given by:
P=mv..
It measures the quantity of movement of the body. The greater is m or v of the body , the greater is its momentum.
Its units in the MKS system is Kg m/s.
There is a principle of conservation of momentum which says:
The total momentum of a system of bodies is conserved if there is no resultant external force acting on the system, although there are interactions(internal forces of action and reaction) between the bodies of the system
Kinetic energy K of a material body of mass m and moving with velocity v is given by : K=(1/2) m v^2.
It measures the energy of the body due to its motion or it is the amount of work which this body can do by virtue of its motion before it comes to rest.
Its unit in the MKS system is Joule, same as that of work.
There is no principal of conservation of kinetic energy. Rather there is a principal of conservation of Mechanical energy which states: The total mechanical energy ( sum of Kinetic and potential energies) of a body or a system of bodies is conserved if the forces acting on them are all conservative or there is no dissipative force involved.

Answer 6

Momentum usually labeled as P equals the mass times the velocity of a body.
Kinetic Energy labeled as KE is equal to one half of the mass times the square of the velocity.