## Newton’s Third Law of Motion

Newton’s second law tells us the magnitude of acceleration which is produced by a force when applied on an object.

These two laws do not tell how the force acts on the object. To answer this question let us study Newton’s third law of motion, which states:

In other words, if an object exerts a force on another object, then in return it will exert a force of the same magnitude on it in the opposite direction (Fig. 2.9).

**Example 1:** A boy throws a ball on the ground. In this case ball exerts a force on the ground. As a result, the ground exerts an equal and opposite force on the ball which makes the ball bounce.

**Example 2:** Let us consider a day-to-day example. While walking on the floor we exert a force by our feet to push the ground backward, in return the ground exerts a force of the same magnitude on our feet forward which makes us move forward. Here our force is called action and the force by ground is called reaction.

The linear momentum of an object is the product of its mass and velocity. To understand it better, let us elaborate on it.

**Illustration**

Let two objects with different masses move with the same velocity. When they are brought to a stop, the one with more mass will require more force to stop as compared to the lighter one.

Now consider two moving objects of the same masses but different velocities. When they are brought to a stop the one with higher velocity will require more force to stop as compared to the slower one.

This concludes that the force needed to stop an object at a particular time depends on both the product of the mass and velocity of a moving object. The product of mass and velocity of a moving body is known as linear momentum or momentum. It is represented by a symbol p.

Let the mass of an object be m. It is moving with velocity v, then linear momentum is

p = mv

Linear momentum is a vector quantity as it has the direction of the motion of the body.

**Unit**

As we know

Unit of momentum = unit of mass × unit of velocity = kg × m/s

S.I. unit of momentum is kg m/s

C.G.S. unit of momentum is g cm/s

**Change in Momentum**

The change in momentum equals the mass times the change in velocity.

∆p = m (∆v)

Where ∆ denotes a small change in the quantity.

The change in product mv can be due to the change in mass m change in velocity v or change in both m and v.

The symbol ∆ before mv denotes a small change in the product of m and v. If mass m does not change, then the product mv will change only due to the change in v and so m can be written before the symbol ∆. The quantity ∆v now represents a small change in velocity only.

The velocity of a moving object is changed when a force is applied to it. Thus, a change in velocity results in a change in momentum.

**Equation**

Let F = force applied on an object

m = Mass of the object

t = time

Suppose its velocity changes from u to v in time t

The initial momentum of an object = mu

Final momentum of an object = mv

Change in momentum in t second = mv − mu

= m (v − u)

\(\text { Rate of change of momentum }=\frac{\text { change in momentum }}{\text { time }}\)= \(\frac{m(v-u)}{t}\) (1)

\(\text { Acceleration } a=\frac{\text { change in velocity }}{\text { time }}\)i.e. a = \(\frac{v-u}{t}\)

Therefore, in equation (1) the omes rate of change of momentum = mass × acceleration = m.a