# Applied Mathematics Newton's laws by DHarperii

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```									Handout 9 Newton’s laws of motion

Newton’s First Law: Inertia

Every object in a state of uniform motion, relative to a
basic frame of reference, tends to remain in that state of
motion unless an external force is applied to it.

This is sometimes stated as “a body initially at rest will remain at rest unless an external force is applied
to it”. It can be used as a deﬁnition of the basic frame of reference.

Newton’s Second Law: Motion

Relative to a basic frame of reference, a particle of mass m
subject to a force F moves in accordance with the equation

F = ma

where a is its acceleration.

This is the most powerful of Newton’s three Laws, because it allows quantitative calculations of dynamics:
how velocities change when forces are applied.

Newton’s Third Law of Motion: Action and Reaction

For every action there is an equal and opposite reaction.

When two particles exert forces on one another, these forces are equal in magnitude and opposite in
sense and act along the line joining the particles.
This law is exempliﬁed by what happens if we step oﬀ a boat onto the bank of a lake: as we move in the
direction of the shore, the boat tends to move in the opposite direction.

Notes.

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