Momentum

Momentum is the name given to a physical quantity that allows us to determine what happens when two moving bodies collide. Momentum is the product of mass and velocity. The equation of momentum is:

p=m×vp = m \times vp=m×v

where
ppp is the momentum,
mmm is the mass, and
vvv is the velocity.

The unit of momentum is kg m/s. Momentum is a vector quantity. The direction of the momentum of a body is the same as the velocity of the body.

Example 1:

A tennis ball of mass 0.5 kg moves with a velocity of 5 m/s. What is the momentum possessed by the tennis ball?

• Putting it into the equation,

p=0.5×5=2.5 kg m/sp = 0.5 \times 5 = 2.5 \text{ kg m/s}p=0.5×5=2.5 kg m/s

Example 2:

A snooker ball of mass 0.6 kg moves with a velocity of 5 m/s. What is the momentum possessed by the snooker ball?

• Putting it into the equation,

p=0.6×5=3 kg m/sp = 0.6 \times 5 = 3 \text{ kg m/s}p=0.6×5=3 kg m/s

Change of Momentum

Change in momentum is equal to final momentum minus the initial momentum. The equation that we use to calculate the change of momentum is:

mv−mumv - mumv−mu

The ball of mass 0.5 kg has an initial velocity of 5 m/s and a final velocity of 10 m/s. What is the change in momentum of the ball?

• Putting it into the equation,

0.5×10−0.5×5=2.50.5 \times 10 - 0.5 \times 5 = 2.50.5×10−0.5×5=2.5

We also call the change in momentum impulse. The formula to calculate impulse is:

F×tF \times tF×t

and

F×t=mv−muF \times t = mv - muF×t=mv−mu

Newton's Second Law and Momentum

The rate of change of an object's momentum is directly proportional to the resultant force acting on the object.

F=mv−mutF = \frac{mv - mu}{t}F=tmv−mu​

Collision

There are two types of collision:

Elastic Collision

A collision is said to be elastic if the total kinetic energy after the collision is equal to that before the collision. Therefore, kinetic energy and momentum before and after collision stay conserved.

Inelastic Collision

A collision is said to be inelastic if the kinetic energy before the collision is not equal to that after the collision, but the momentum stays conserved.

Total momentum before collision=Total momentum after the collision\text{Total momentum before collision} = \text{Total momentum after the collision}Total momentum before collision=Total momentum after the collision