Newton's laws of motion

First law

: An object at rest or in a state of uniform motion will remain at rest or in uniform motion, unless acted upon by a net external force.

This is also known as the law of inertia. Inertial motion is a motion with the constant velocity. Thus, a force always produces a change in velocity, or, in other words, an acceleration.

Second law

: The acceleration of an object is proportional to the net force applied to it.

The coefficient of proportionality is called the inertial mass. Mathematically, the second law is expressed like this:

$$\vec{F} = m\vec{a}.$$

Linear momentum

A linear momentum is a very important characteristic of an object in mechanics. It is a product of the object's mass and its velocity:

$$\vec{p} = m\vec{v}.$$

Since the change in velocity is acceleration:

$$\vec{a} = \left\{\cal CHANGE\ IN\right\} \vec{v},$$

the change in momentum is then the force:

$$\vec{F} = \left\{\cal CHANGE\ IN\right\} \vec{p}.$$

Important case: in the absence of the net external force the linear momentum of an object is conserved.

This is called the law of conservation of momentum. It is more general than the law of inertia, because it is a combination of the first and the second Newton's laws .

An empty, freely rolling boxcar is suddenly loaded with a load of coal twice the mass of an empty boxcar. How will the speed of the boxcar change?

A:

It will not change.

B:

It will be half of the original speed.

C:

It will be third of the original speed.

D:

It will be twice the original speed.

Third law

: For every action, there is an equal and opposite reaction.

If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.