Newton's Third law

Newton's Third Law of Motion

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

Mathematically, this law is expressed as:

Where:

• F₁ is the force exerted by the first object on the second object, and

• F₂ is the force exerted by the second object on the first object.

This law implies that forces always occur in pairs. When one object pushes or pulls another object, the second object pushes or pulls back with an equal force in the opposite direction.

Derivation:

To derive Newton's third law, consider two objects, object 1 and object 2, interacting with each other. According to Newton's second law, the force exerted by object 1 on object 2 is given by:

Where is the mass of object 1 and is its acceleration.

Similarly, the force exerted by object 2 on object 1 is given by:

Where is the mass of object 2 and is its acceleration.

Now, according to Newton's second law, the accelerations of object 1 and object 2 are related to the forces and masses as:

From these equations, we can see that:

This demonstrates that the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1, thus confirming Newton's third law of motion.

Therefore, Newton's third law of motion states that forces always occur in pairs, and for every action, there is an equal and opposite reaction.