Momentum is defined as the quantity of motion that a body has.

It is measured as the product of its mass and its velocity.

Momentum = Mass x Velocity

p = m x v

Mass – kg

Velocity – m/s

Momentum – kg m/s

Since velocity is a vector quantity (it could have a negative value), momentum is also a vector quantity, meaning that it can also be negative.

**Example:**

A truck of mass 2 tonnes is moving at a velocity of 45 km/h. Find its momentum.

Solution:

Mass = 2 tonne = 2 x 1000 kg = 2000 kg

Velocity = 45 km/h = (45 x 5) ÷ 18 = 12.5 m/s

p = m x v

p = 2000 x 12.5

p = 25,000 kg m/s

### Conservation of Momentum

For two bodies, A and B, colliding in an isolated system, the total momentum before and after the collision is conserved.

A popular example of this is a car crash.

Imagine two cars travelling in opposite directions towards each other. Each car would have its own momentum.

When they crash with each other, the sum of their momentums before collision would be equal to the sum of their momentums after collisions.

It would be simpler if we use an example.

**Example:
**Two cars, A and B are travelling towards each other.

A has a mass of 200 kg and a velocity of 10 m/s.

B has a mass of 400 kg and a velocity of 8 m/s.

I) Calculate their individual momentums

II) Calculate their momentums after the collision

After the collision, the cars stick together and move as one.

III) Calculate the velocity of both cars after the collision.

Solution (I):

Momentum of A = 200 x 10 = 2000 kg m/s

Since B is travelling in the opposite direction, its velocity would be negative.

Momentum of B = 400 x (-8) = -3200 kg m/s

Solution (II):

Sum of momentum before collision = p(A) + p(B)

∑p = p(A) + p(B) = 2000 + (-3200) = -1200 kg m/s

According to the law of conservation of momentum,

total momentum before collision = total momentum after collision

So total momentum after collision = -1200 kg m/s

Solution (III):

Momentum is conserved.

Since the cars stick together, their velocity would be v (AB).

Mass (AB) = 200 + 400 = 600 kg

∑p = m (AB) x v (AB)

-1200 = 600 x v (AB)

v (AB) = -1200 ÷ 600

v (AB) = -2 m/s

The negative sign indicates that both cars are moving from right to left.