Addition of Momenta

Just like other vectors, we can add linear momentum vectors. The sum of all momenta of a system of individual objects (1, 2, ..., n) is called the total momentum, :

= $\sum$_i=1,...,n

_i =

₁ +

₂ +

₃ + ... +

The total momentum and the sum of the velocities of a system of objects do not need to point in the same direction, as the following example shows.

Question:

A car of mass 700 kg is traveling with velocity +65 mi/h on a road. In opposite direction approaches a 4500 kg truck with velocity -65 mi/h. What is the total momentum of the system?

Answer:

Adding the velocity vectors yields _t+ _c = 0 mi/h. Since the velocities add up to 0, will the same be true for the momentum vectors? Of course not!
The momentum of the car is _c = m_c _c= 20,000 kg m/s

The momentum of the truck is _t = m_t _t= -131,000 kg m/s (negative because v is to the left)

The total momentum is therefore = _c + _t = -111,000 kg m/s