How Newton's Laws of Motion Work

By: William Harris  | 

Applications and Limitations of Newton's Laws

Does the moon move around the Earth in the same way that a stone whirls around the end of a string?
Does the moon move around the Earth in the same way that a stone whirls around the end of a string?
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By themselves, the three laws of motion are a crowning achievement, but Newton didn't stop there. He took those ideas and applied them to a problem that had stumped scientists for years -- the motion of planets. Copernicus placed the sun at the center of a family of orbiting planets and moons, while the German astronomer Johannes Kepler proved that the shape of planetary orbits was elliptical, not circular. But no one had been able to explain the mechanics behind this motion. Then, as the story goes, Newton saw an apple fall to the ground and was seized by inspiration. Could a falling apple be related to a revolving planet or moon? Newton believed so. This was his thought process to prove it:

  1. An apple falling to the ground must be under the influence of a force, according to his second law. That force is gravity, which causes the apple to accelerate toward Earth's center.
  2. Newton reasoned that the moon might be under the influence of Earth's gravity, as well, but he had to explain why the moon didn't fall into Earth. Unlike the falling apple, it moved parallel to Earth's surface.
  3. What if, he wondered, the moon moved about the earth in the same way as a stone whirled around at the end of a string? If the holder of the string let go -- and therefore stopped applying a force -- the stone would obey the law of inertia and continue traveling in a straight line, like a tangent extending from the circumference of the circle.
  4. But if the holder of the string didn't let go, the stone would travel in a circular path, like the face of a clock. In one instant, the stone would be at 12 o'clock. In the next, it would be at 3 o'clock. A force is required to pull the stone inward so it continues its circular path or orbit. The force comes from the holder of the string.
  5. Next, Newton reasoned that the moon orbiting Earth was the same as the stone whirling around on its string. Earth behaved as the holder of the string, exerting an inward-directed force on the moon. This force was balanced by the moon's inertia, which tried to keep the moon moving in a straight-line tangent to the circular path.
  6. Finally, Newton extended this line of reasoning to any of the planets revolving around the sun. Each planet has inertial motion balanced by a gravitational attraction coming from the center of the sun.

It was a stunning insight -- one that eventually led to the universal law of gravitation. According to this law, any two objects in the universe attract each other with a force that depends on two things: the masses of the interacting objects and the distance between them. More massive objects have bigger gravitational attractions. Distance diminishes this attraction. Newton expressed this mathematically in this equation:


F = G(m1m2/r2)

where F is the force of gravity between masses m1 and m2, G is a universal constant and r is the distance between the centers of both masses.

Over the years, scientists in just about every discipline have tested Newton's laws of motion and found them to be amazingly predictive and reliable. But there are two instances where Newtonian physics break down. The first involves objects traveling at or near the speed of light. The second problem comes when Newton's laws are applied to very small objects, such as atoms or subatomic particles that fall in the realm of quantum mechanics.

Still, these limitations shouldn't take away from his accomplishments, so flip to the next page for more information about Isaac Newton and other geniuses.

Originally Published: Jul 29, 2008

Newton's Laws of Motion FAQ

What are Newton's three laws of motion called?
These three laws form the foundation of classical mechanics, the science concerned with the motion of bodies being acted upon by forces.
What is Newton's second law?
Newton's second law of motion states that force is equal to the change in momentum per the change in time. For a constant mass, force equals mass times acceleration.
What is Newton's first law of motion?
The law of inertia states that an object at rest will stay at rest, forever, as long as nothing pushes or pulls on it. An object in motion will stay in motion, traveling in a straight line, forever, until something (a force) pushes or pulls on it.
What is Newton's third law of motion?
It is the law of force pairs: Every force involves the interaction of two objects. When one object exerts a force on a second object, the second object also exerts a force on the first object. The two forces are equal in strength and oriented in opposite directions.

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