Physics

# An Explanation of Newtons three Laws of Motion

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In 1687, Sir Isaac Newton published the Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). It was quickly recognised as one of the most important scientific works ever written. For the first time in human history, the behaviour of moving objects had been reliably and predictably explained.

The three laws of motion first introduced in this book form the foundations of classical mechanics. Even in today's quantum universe, these three laws of motion still hold valid in our everyday world.

First Law of Motion

A body at rest stays at rest and a body in motion stays in motion unless acted upon by an external force.

Items with mass do not start to move unless they are subjected to a force. Bodies which are already moving will continue to move in the same direction and with the same speed unless subjected to a force which changes either their speed or direction. (Friction counts as a force.) For this reason, Newton's first law of motion is sometimes called the law of inertia.

The common version of this law simplifies the vector sum of forces into a single external force. If all active forces completely balance each other out, it is the same as if no force were acting. In this case, we say that the vector sum of forces equals zero. In physics, a vector combines magnitude with direction. Two forces acting on an object will not cancel each other out unless they are pushing or pulling equally hard in opposite directions.

Second Law of Motion

A body acted upon by a force will accelerate proportionally to its mass and the force applied.

Mathematically, this is expressed as F = ma, where F represents the applied force, m represents the mass of the object, and a represents the resulting acceleration of the object. Actually, by introducing acceleration, this becomes a derivative equation examining force relative to the time derivative of momentum m(dv/dt), but we don't need to drag calculus into this to understand its point.

Basically, it means that the more force you apply to an object with constant mass, the greater the acceleration. A larger mass subjected to the same force will not accelerate as rapidly as a smaller mass. A train starts up much more slowly than a car, and also takes much longer to come to a complete stop.

Note that in physics, acceleration refers to any change in velocity: slowing down, speeding up, or changing direction. This is because velocity is not just speed, but a combination of speed and direction. Similarly, the force is not just the push or pull applied but also its direction. The direction of a force relative to the current movement of the object matters. A force applied opposite the current movement of the object will slow it down. A force applied at a slant to the current movement of the object will change its direction.

A more complicated version of the second law of motion allows for mass to change during acceleration. It happens all the time in regular life, such as when hard-braking tires are stripped bald by the pavement (loss of mass) or when ice shavings build up in front of braking skates (gain of mass). Sometimes the amount is trivial. Other times the amount is considerable: racecars get lighter and accelerate faster as they use up fuel. Once again, we have to drag calculus into it to deal with the change of mass relative to time (dm/dt), plus we also have to add a term (u) to account for the momentum of the lost or gained mass.

Third Law of Motion

To every action, there is an equal and opposite reaction.

If a force is applied by one object to another, then the second object also applies the exact opposite force to the first. The earth pulls down on us, but we also press against the earth. If the forces were not equal, we might keep sinking into the earth until we reach a dense enough layer to provide enough resistance to stop us: at which point the forces are balanced.

A simpler example can be seen in stepping from an unsecured boat onto a dock. In stepping forward with one foot, the other foot pushes back, pushing the boat away. The reactions are equal, but their effects need not be. The boat might be forced back much further than the single step we are trying to take onto the dock. If we are not careful, ker-splash!

Space travel uses Newton's third law of motion to achieve escape velocity. By flinging a part of its mass downward toward the earth at high velocity, the equal and opposite reaction forces the rocket upward. Exactly the same effect can be seen by releasing the neck of an inflated rubber balloon, suddenly releasing the air. Of course, both the balloon's and the rocket's masses are constantly changing at the same time, making this a much more complex equation than it seems on the surface.

The three laws of motion are neither universal nor absolute. Rather, they should be considered excellent approximations for the everyday world. They fail at molecular and smaller scales where quantum factors begin to predominate, at very high speeds where special relativity applies, and in high gravitational fields where general relativity takes over.

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