Newton’s Laws of Motion

Newton’s laws of motion are three laws of classical mechanics that describe the relationship between the motion of an object and the forces acting upon it.

1. A body in motion remains in motion or a body at rest remains at rest, unless acted upon by a force.
2. Force equals mass time acceleration: F = m*a. Or, the rate of change of a body’s momentum equals the force acting upon it: F = Δp/Δt.
3. For every action, there is an equal and opposite reaction.

History

Sir Isaac Newton describes the three laws of motion in his 1687 book Philosophiae Naturalis Principia Mathematica. The Principia also outlines the theory of gravity. While the Theory of Relativity applies to objects moving near the speed of light, Newton’s laws work well under ordinary conditions.

Newton’s First Law – Inertia

An object at rest remains at rest or an object in motion remains in motion at constant speed and in a straight line, unless acted upon by an unbalanced force.

Basically, the first law describes inertia, which is a body’s resistance to a change in its state of motion. If no net force acts on a body (all external forces cancel out), then the object maintains constant velocity. A motionless object has a velocity of zero, while a moving body has a non-zero velocity. An external force acting upon an object changes its velocity.

Here are some examples of Newton’s first law:

• A dropped ball continues falling
• If you let go of a moving cart, it continues rolling (ultimately stopped by friction)
• An apple resting on a table does not spontaneously move

Newton’s Second Law – Force

The rate of change of an object’s momentum equals the force acting upon it or the applied force equal’s an object’s mass times its acceleration.

The two equations for Newton’s second law are:

F = m*a

F = Δp/Δt

Here, F is the applied force, m is mass, a is acceleration, p is momentum, and t is time. Note that the second law tells us that an external force accelerates an object. The amount of acceleration is inversely proportional to its mass, so it’s harder to accelerate a heavier object than a lighter one. The second law assumes an object has constant mass (which is not always the case in relativistic physics).

Here are examples of Newton’s second law:

• It takes more effort moving a heavy box than a light one.
• A truck takes longer to stop than a car.
• It hurts more getting hit with a fast-moving baseball than a slow one. Each ball has the same mass, but the force depends on the acceleration.

Newton’s Third Law – Action and Reaction

When one object exerts a force on a second object, the second object exerts and equal and opposite force on the first object.

For every action, there is an equal and opposite reaction. So, if set an apple on a table, the table pushes up on the apple with a force equal to the mass of the apple times the acceleration due to gravity. This can be difficult to visualize, but there are more obvious examples of Newton’s third law:

• If you are wearing roller skates and you push another person wearing skates, you both move.
• A jet engine produces thrust. As the hot gases exit the engine, an equal force pushes the jet forward.

References

• Halliday, David; Krane, Kenneth S.; Resnick, Robert (2001). Physics Volume 1 (5th ed.). Wiley. ISBN 978-0471320579.
• Knight, Randall D. (2008). Physics for Scientists and Engineers: A Strategic Approach (2nd ed.). Addison-Wesley. ISBN 978-0805327366.
• Plastino, Angel R.; Muzzio, Juan C. (1992). “On the use and abuse of Newton’s second law for variable mass problems”. Celestial Mechanics and Dynamical Astronomy. 53 (3): 227–232. doi:10.1007/BF00052611
• Thornton, Stephen T.; Marion, Jerry B. (2004). Classical Dynamics of Particles and Systems (5th ed.). Brooke Cole. ISBN 0-534-40896-6.