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# Newton and the Mechanical Laws of Motion

I. Newton
(1642-1727)

Isaac Newton embraced Galileo's Principle of Relativity. Newton developed his Laws of Motion, which respected the Galilean Principle of Relativity.

NEWTON'S LAW OF INERTIA
A body, not acted on by any force, remains in uniform motion.

NEWTON'S LAW OF MOTION
Moving an object with twice the mass will require twice the force.
Force is proportional to the mass of an object and
to the acceleration (the change in velocity).
F=ma.

Newton's statements are APPROXIMATELY TRUE. For practical purposes (i.e., everyday life), we can (and usually do) take them to be TRUE.

## Newton's Mechanics and Galileo's Relativity

Newton's Law of Inertia and Law of Motion are mechanical laws of physics, and should respect the Galileo Principle of Relativity.

That is to say:

• Newton's Law of Inertia tells us that "the worldline of an undisturbed object is a straight line". If it repsects Galileo's democratic Principle of Relativity, then all inertial observers should see the worldline of that object as straight. Indeed, this is true.

Newton's Law of Inertia respects the Galileo Principle of Relativity
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This is the same animation from Galileo's Spacetime

• Newton's Law of Motion tells us that "the worldline of an object with a given mass experiencing a constant force is a parabola (which is completely determined by knowing the mass and the force)". If it repsects Galileo's democratic Principle of Relativity, then all inertial observers should see the worldline of that object to be the same parabola. Indeed, this too is true.

Newton's Law of Motion respects the Galileo Principle of Relativity
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The white curve is the worldline of the above object. It is a parabola The red curve is a congruent parabola, drawn in just to show that the original parabola has not changed under the transformation.

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