Newton's first law states that, if no net external force acts on a body at rest, that body will continue to remain at rest. If no net external force acts on a body moving in a straight line at constant velocity, that body will continue to move in a straight line at constant velocity.

Newton's second law states that, when a force acts on a particle, this force is equal to mass times acceleration.

Where:

We can also write the second of Newton's Laws for a system of particles:

Where:

Note that there is no restriction in the way the particles are connected. As a result, the above equation will also hold true for a rigid body, a deforming body, a liquid, or a gas system.

For proof of the above equation see Newton's Second Law.

Newton's third law states that, for every action there is an equal and opposite reaction. This means that, when two bodies are in contact, the reactions between those bodies are equal in magnitude and opposite in direction. The figure below shows an example of two bodies in contact.

If we were to isolate each body, the reactions acting on them will be equal and opposite. The figure below shows a general example of the reactions acting on each body.

where

The resultant vertical force acting on each body is the sum of all the forces acting in the vertical direction, along the contact surface.

The resultant horizontal force acting on each body is the sum of all the forces acting in the horizontal direction, along the contact surface.

The resultant moment (torque) acting on each body is the sum of all the torques, along the contact surface. The torques are caused by equal forces acting in opposite directions. For example, the figure below shows equal forces

From this, the moment (torque) is calculated as:

The moment

In general, when solving real world physics problems, every contact surface (or contact point) between one body and another body can be replaced with a single resultant force

Note that for some cases, there will only be a resultant force

For example, a lubricated ball and socket joint cannot resist twisting, so it has no moment

The main advantage of replacing a contact surface (or contact point) with a single resultant force

Another way to look at it is as follows: The general motion of a body always consists of translation and rotation. The resultant forces

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