Coaster Dynamics: Physics Primer Chapter 9



Coaster Dynamics
Physics Primer

Chapter 9

Newton's Third Law of Motion

When developing his laws of motion, Newton recognized that a force could not exist independently. He realized that forces could only exist due to an interaction of objects.

For instance, when a baseball bat hits a baseball, it exerts a force on the ball -- and as a result, the ball is accelerated. At the same time, the bat receives a force from the ball -- causing the bat to slow down or stop. Anyone who has played baseball has experienced this interaction.

Newton identified the symmetry of action and reaction forces, and stated it in his Third Law of Motion:

  Newton's Third Law of Motion:

The mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

In language more common for today, this can be restated as:

For every action, there is an equal and opposite reaction.
or
Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Note that the action and reaction forces do not cancel each other out, because they act on different objects. For instance, the baseball exerts an action force in the bat... and the bat exerts a reaction force on the ball. If the action and reaction forces acted on the same object, the net force would sum to zero, and the resulting acceleration would be zero.

Action/Reaction Forces and Reference Frames

Although Newton didn't fully exploit the concept at the time, the Third Law of Motion is a consequence of, and thus a restatement of, the Equivalence of Reference Frames.

Action and reaction forces must both exist... and it doesn't matter which force we choose to call the action and reaction. If viewed from a reference frame attached to the baseball, the bat moves toward the ball and exerts a force on the ball. On the other hand, if viewed from a reference frame attached to the bat, the ball moves toward the bat and exerts a force on the bat. In either case, because the same laws of motion must be valid in both reference frames, the forces must be of equal magnitude and in opposite directions.

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