Newton’s Laws of Motion - Newton's Third Law of Motion

Force is a reciprocal action between two objects, meaning forces always exist in pairs in nature. When one object applies a force on a second object, the second object simultaneously applies a force back on the first. These forces are always equal in magnitude and opposite in direction. This fundamental idea about force pairs is expressed in Newton's third law of motion. The force applied by the first object is called the action force, and the force applied by the second object is called the reaction force.

"Every action force has an equal and opposite reaction force which acts simultaneously."

The concise law statement is: "To every action (force), there is an equal and opposite reaction (force)."

1. Reciprocal Nature of Force: When one object exerts a force on another, the second object exerts an equal force in the opposite direction on the first. These forces are simultaneous.
2. Action and Reaction Forces: The force exerted by the first object is called the action force, and the force exerted by the second object in response is the reaction force.
3. Characteristics of Action and Reaction Forces: They are equal in magnitude but opposite in direction and act on different objects, not the same one. They occur simultaneously, meaning one does not "cause" the other; both occur at the same time.
4. Forces on Different Objects: Action and reaction forces are always on different objects.
5. No Cancellation: There is no question of cancellation of these forces because they are experienced by different objects.
6. Contact Not Necessary: The action-reaction pair need not be contact forces.

• Action Force Exerted: A body x exerts an action force on body y, written as \[F_{y\leftarrow x}\]. This is the force experienced by y.

• Reaction Force Exerted: As a result, body y exerts a reaction force \[F_{x\leftarrow y}\] on body x. This is the force experienced by x.

• No Cancellation: Forces\[F_{x\leftarrow y}\] and \[F_{y\leftarrow x}\] are equal in magnitude and opposite in their directions.

• Distinct Objects: These forces do not cancel because they are experienced by different objects (one on x and one on y).

• It defines action and reaction as a pair of equal and opposite forces acting along the same line.
• It establishes that action and reaction forces are always on different objects.
• It explains why a pair of forces does not cancel each other (because they act on different objects).
• It shows that the law applies to both contact and noncontact forces.

\[\vec{F}=\frac{d\vec{p}}{dt}=\frac{d\left(m\vec{\mathrm{v}}\right)}{dt}\]

Hose Pipe Recoil:

When a hose pipe ejects water horizontally, the ejecting water is the action force on the water. The water then exerts a backward force (recoil force) on the pipe as the reaction force.

 Noncontact Forces

• Magnets: Repulsive forces between two magnets (the two magnets are not in contact).
• Celestial Bodies: Gravitational force between Earth and Moon or between Earth and Sun.