**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.

- A body in motion remains in motion or a body at rest remains at rest, unless acted upon by a force.
- Force equals mass times acceleration: F = m*a. Or, the rate of change of a body’s momentum equals the force acting upon it: F = Δp/Δt.
- 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 P*articles and Systems (5th ed.). Brooke Cole. ISBN 0-534-40896-6.