#### Linear Momentum

The product of mass and velocity is called momentum.

It is a vector - has both magnitude and direction - and its units are **kgms ^{-1}**.

**momentum = mass x velocity**

momentum = mv

momentum = mv

**E.g.1**

The mass of an object is 5kb and velocity is 2 ms^{-1}. Find its momentum.

momentum = 5 x 2 = 10 kgms^{-1}

**E.g.2**

The mass of an object is 2 kg. It moves towards a wall at 20 ms^{-1}, hits the wall and bounces back at 10 ms^{-1}. Find the change in momentum.

momentum towards the wall = 2 x 20 = 40 kgms^{-1}

momentum away from the wall after the impact = 2 x 10 = 20 kgms^{-1}

Change in momentum = 40 - -20 = 60 kgms^{-1} towards the wall.

#### The Principle of Conservation of Linear Momentum

When two of more objects collide, the total momentum, before and after the collision, remains the same, in the absence of external forces.

Case 1

Two objects of mass 3 kg an 2 kg move at 10 ms^{-1} and 5ms^{-1} respectively in the same direction. After impact, they move as a single combined object. Find its speed.

Case 2

Two objects of mass 3 kg an 2 kg move at 10 ms^{-1} and 5ms^{-1} respectively in the opposite directions. After impact, they move as a single combined object. Find its speed.

Case 3

Two objects of mass 3 kg an 2 kg move at 30 ms^{-1} and 5ms^{-1} respectively in the opposite directions. After impact, the heavier object reverses the direction
at 10 ms^{-1}. Find the speed of the other object and the direction.

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**Now work out the following to complement what you have learnt so far.**

- Masses of two object are 3 kg and 2 kg
respectively. They move in opposite directions at 20 ms
^{-1}and 2 ms^{-1}respectively. After the collision, the lighter object reverses its motion with the speed being the same. Determine the subsequent motion of the heavier object. - Three spheres of the same radii are
placed in a straight line on a smooth table. Their masses are 2kg, 5kg and 6kg respectively. The first one moves at 'u'
ms
^{-1}and hits the second one. On impact, the speed of the second one becomes 'u'. Then the second one hits the third one, and on impact, the speed of the third one becomes 'u'. Find whether the first one and the second one would collide again. - -1 and hits a wall. After 0.5 seconds, it reverses the direction at 5 ms
^{-1}. Find the change in momentum and hence calculate the force exerted on the wall. - Two objects of mass 2 kg and 5 kg move towards each other at 20ms
^{-1}and 10 ms^{-1}respectively. After the impact, they move as a single object. Find its speed.