# Newton's Laws

### Newton's Three Laws of Motion

#### Newton's First Law of Motion

*"A body continues in a state of rest, or of uniform motion in a straight line, unless acted upon by an external force."*

In other words, an object remains at rest or moves at constant velocity when

Newton’s first law is based on the principle of inertia. The tendency of a body to resist a change in its state of motion is called **inertia**.

#### Newton's Second Law of Motion

*"An object of mass moves with an acceleration that is defined by ."*

Thus, the acceleration of a body is directly proportional to the net force acting on the body, and is inversely proportional to its mass.

#### Newton's Third Law of Motion

*"For every action there is an equal and opposite reaction."*

In other words, if body applies a force on body , then body applies an equal and opposite force on body .

Convention for the subscripts: If a force is exerted by an object A on an object B then we write this force as follows:

http://www.youtube.com/watch?v=KeNye0nTqmM

- Focus on notation: The first subscript indicates the particle which exerts the force; the second subscript indicates the particle on which the force is exerted. For example, the normal force exerted by the floor () on a box () in the diagram below should be labelled

- Action/reaction pairs: The two forces and form an action-reaction pair if and only if the two forces are of the same type (a normal force and a gravitational force cannot be an action-reaction pair) and if and only if we can write that

__For example:__ which is a gravitational force exerted by the Earth on the man and which is a gravitational force exerted by the man on the Earth are the action-reaction pair.

On the other hand, which is a gravitational force exerted by the Earth on the man and which is the normal force exerted by the surface of the Earth on the man are not the action-reaction pair.

- Application of these concepts to find the acceleration of systems — problem solving strategy:

- Define a system of particles that you will study — each particle should be dealt with separately;
- List external forces acting on each particle use the notation which indicates the agent and then draw arrows to represent each external force in the diagram;
- Draw a free body diagram for each particle:
- Select and draw an "appropriate" coordinate system for each particle so that
- The x-axis is parallel to the direction in which a particle may possibly move or the direction of possible acceleration;
- The orientation of the x-axis for each particle in the system must be in the same sense;
- The positive y-axis is oriented +90º from the positive x-axis.

- Transfer the arrows representing forces into this system (each arrow has the tail at the origin).
- Determine the angle each arrow makes with the positive x-axis.

- Select and draw an "appropriate" coordinate system for each particle so that
- Write all forces in terms of their x- and y-components: for a given force of magnitude and direction , and
- Write equations for each particle or
- Write equations for each particle
- Identify all the action-reaction pairs.
- Solve the system of equations.

- An overview of the forces acting on a body in a mechanical system:

- Gravitational force:
- Special case of a gravitational force (close to the surface of Earth):
- Contact forces: Tension, Normal force and Friction.
- Force of a spring: restoring force
- Tension is caused by a restoring force acting between particles of thin long objects: rope, rod, beam, string, etc.
- The direction of the tension is always parallel to the thin object.
- Normal force is caused by a restoring force acting between particles of surfaces; it is always perpendicular to the surface.
- Friction occurs when two surfaces are in contact. It is due to an interaction between surface particles of one object and surface particles of the second object.