Momentum
Forces and Motion

# Momentum

Glossary Definition for 16-19 ## Description

Momentum is a vector quantity associated with motion. In a system upon which no external forces act, total momentum is conserved.

Momentum is usually represented by the symbol p.

In Newtonian mechanics, momentum, p, of an object is defined as the product of the mass, m, and the velocity, v, of the object:

p = mv

Massless particles can also have momentum. For example, a photon has momentum whose magnitude, p, is related to its energy, E, which in turn is related to the frequency, f, and wavelength λ, of the corresponding electromagnetic wave:

p = Ec = hfc = hλ

where h is the Planck constant and c the speed of light in a vacuum.

## Discussion

The momentum of an object is, intuitively, a measure of how much effort one has to make to alter its motion. Given that force is the rate of change of momentum, an object of small mass going quickly can require as much force, applied over the same time (i.e. the same impulse) to stop it as an object of larger mass going more slowly.

The definition of momentum as mv works well in the Newtonian regime at speeds well below the speed of light. The more general definition, which works at all speeds, is

p = γm0v

where m0 is mass of the object when at rest and

γ =     1 (1-v 2c 2)

In the limit v << c, we have γ~1, so that the above expression reduces to the Newtonian version. The importance of momentum is that, for an isolated system, it is conserved in all circumstances. It does not matter how complicated the interactions between different particles are, the total momentum of the system will always be the same before and after the interaction, provided no external forces act upon it. If a constant resultant force F acts upon an object over a time period Δt, the object’s momentum will be changed by an amount Δp = FΔt is the impulse imparted to the object.

N s

kg m s-1

## Mathematical expressions

• In Newtonian mechanics, momentum, p, is defined as the product of the mass, m, and the velocity, v, of an object:

p = mv
• More generally, massless particles can also have momentum. For example, a photon has momentum whose magnitude, p, is related to its energy, E, which in turn is related to the frequency, f, and wavelength, λ, of the corresponding electromagnetic wave:

p = Ec = hfc = hλ

where h is the Planck constant and c is the speed of light in a vacuum

## Related entries

• Force
• Impluse
• Kinetic energy

## In context

A photon of visible light with wavelength 660 nm has momentum p = 10-27kg m s-1

An electron travelling through a cathode ray tube at about 106 m s-1 has p = 10-24kg m s-1

A sprinter of mass 70 kg running at 10 m s-1 has p = 700 kg m s-1

In 2013, meteorite fragments crashed to Earth near the Russian city of Chelyabinsk. The largest fragment had a mass over 570 kg. When it was travelling at about 20 m s-1 (typical of large meteorites) its momentum was about 1.1 × 104 kg m s-1.

## Reference

• http://cams.seti.org/Popova2013-ms.pdf
###### Momentum
appears in the relation p=mv F=dp/dt λ=h/p ΔxΔp>ℏ/2
has the special case Angular Momentum