Course content Course content
Collisions and conservation laws
Collisions and conservation laws

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Collisions and conservation laws

7.1 Relativistic momentum

According to Einstein’s theory the relativistic momentum of a particle with mass m and velocity bold v is given by

bold p = fraction m bold v over square root 1 minus fraction v squared over c squared end end end
Equation label: (12)

where v is the speed of the particle and c is the speed of light in a vacuum. The speed of light in a vacuum, c = 3.0 times 10 super 8 mathrm mathrm superscript minus 1 end, plays an important role throughout special relativity. Among other things it represents an upper limit to the speed of any particle.

Equation 12 implies that the momentum of a particle increases more rapidly with increasing speed than the Newtonian relation (bold p = m bold v) predicts. This is shown in Figure 6, where the behaviour of the Newtonian and relativistic definitions of momentum magnitude are compared. You can see the good agreement at low speed, but you can also see the increasing discrepancy as the speed increases. Note that the relativistic definition does not extend beyond v = c. This reflects the fact that in special relativity it is impossible to accelerate a particle with mass to the speed of light, as you will soon see.

Figure 6 The magnitude of the momentum of a particle of mass m plotted against the particle’s speed v according to Newtonian mechanics and special relativity. The Newtonian relation closely approximates that of relativity for values of v that are small compared with the speed of light, c.
S217_1
Print Print

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371