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How to Calculate Momentum in Physics

Updated on November 7, 2012

In everyday life, people use the term ‘momentum’ to speak of both abstract and physical things. Here’s an example: “We need to maintain the momentum of our business.” … or, “That 18 wheeler has some serious momentum!”

Something has to be ‘moving’ to have momentum, and in Physics that something has to be physical. So to calculate the momentum of a business wouldn't be practical in the realm of Physics, but for an 18-wheeler screaming down a highway -- absolutely! Momentum is directly related to Isaac Newton’s 2nd law of motion where he says that the rate of change in momentum of a body is directly proportional to the external force that causes it. Therefore:

F=p/t, where F = Force, p = change in momentum and t = time

From that principle, we can break it down even further to say that:

Momentum = mass * velocity
p = mv

In short, the momentum of a body is the product of the mass of the body and the velocity which it possesses.

Source

Calculating momentum of moving trailer

Take for instance, an 18 wheeler of mass 32,000 kg is travelling at 22 m/s. The trailer's momentum would be:

p = mv
= 32,000 kg * 22 m/s
= 704,000 kgm/s

Take note that the unit of momentum (p) is the kilogram meter per second (kgm/s)

Calculating momentum of parked trailer

So since we said that a body has momentum only if its moving, then that is the same as saying a body has no momentum at all once it’s stationary or at rest.

When the trailer is parked, we can safely say (even without calculations) that its momentum is 0 kgm/s.

If its parked, then it’s not moving and has a velocity of 0 m/s. It’s mass is the same whether or not it is parked or moving.

Therefore, momentum of trailer when parked is:
p = mv
= 32,000 kg * 0kgm/s
= 0 kgm/s

Calculating the change in momentum

What if we say that while the trailer was on a highway, it increased its speed from 22 m/s to 54 m/s. What is the change in momentum?

Change in momentum = final momentum - initial momentum

The initial momentum is related to the initial velocity (u) of 22 m/s, whereas the final momentum is related to the final velocity (v) of 54 m/s.

Therefore:
Δp = mv-mu
= (32,000 kg * 54 m/s) - 704,000 kgm/s
= (1,728,000 - 704,000) kgm/s
= 1,204,000 kgm/s

Calculating the rate of change of momentum

If the trailer takes 20 seconds to change it’s speed from 22 m/s to 54 m/s, then what would be the rate of change of momentum of the trailer?

Remember from the beginning, we mentioned that the rate of change of momentum is:
Δp/t
Therefore p is:
= 1,204,000 kgm/s / 20 s
= 512,000 kgm/s2

Be careful with the units for rate of change of momentum and momentum. They are often confused!

The unit for rate of change of momentum is the: kilogram meter per second squared (kgm/s2)

One final thing to make note of: If you were paying attention, then you will also realize that the rate of change of momentum is also equal to the force that caused the change in momentum in the first place. This means that the Force of the Trailer in those 20 seconds was 512,000 kgm/s2 or more simply, in honor of Isaac Newton, 512,000 Newtons.

Momentum is a another mechanical way to describe the motion of bodies on a macro level. In this case, we've looked at the linear momentum of bodies with the example of an 18 wheeler. It can be a treat to make simple calculations of the momentum of different bodies and compare them -- even your own personal bodily momentum! Furthermore, you can calculate the Force of a body by calculating the body’s rate of change of momentum.

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    • theblackedition profile imageAUTHOR

      Shane Brown-Daniels 

      5 years ago from USA

      Great info Chris! It's interesting b/c 'Torque' and 'Moment(s)' are used a lot in Physics -- same quantity. Didn't know of 'Drall'... Thanks.

    • CHRIS57 profile image

      CHRIS57 

      5 years ago from Northern Germany

      I was only wondering about the name of it, which may differ in different languages. What you call "Momentum" in English is "Impuls" in German. However the similar word "Moment" in German is "Torque" in English and last but not least the English "Impulse" is "Drall" in German.

      Whatever the wording may be, i only trust those technical guys who know the difference.

    • theblackedition profile imageAUTHOR

      Shane Brown-Daniels 

      5 years ago from USA

      They are very much related. Impulse is the 'change in momentum' of a body which is equivalent to 'force multiplied by time (of impact)'. Thanks for bringing that up -- I should add it.

    • CHRIS57 profile image

      CHRIS57 

      5 years ago from Northern Germany

      Didn´t know this is called "Momentum". In other languages this is named "Impulse".

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