Newton’s Second Law, originally published in his seminal work Philosophiæ Naturalis Principia Mathematica (Principles of Natural Philosophy), was the middle of three which changed our fundamental understanding of the universe by explaining mathematically how the motion of objects works.
Newton’s Second Law or F=ma
This law is often expressed by the simple equation F=ma where F is force (a vector, which has a direction), m is mass and a is acceleration (also a vector). In words, the force applied to an object is equal to its mass multiplied by the acceleration. Acceleration can be easier to imagine, especially for vectors, as a change in velocity.
The Second Law is very powerful and an essential item in any physicist or engineer’s toolbox. It can be used to describe the motion of more or less anything in classical mechanics by breaking the motion down into a series of velocity changes. Rearranging the formula algebraically means that only two of the quantities are ever needed in order to calculate the third.
Remember Directions!
It is always important to remember to take directions into account when using this law. Take the example of a toy car pushed along a table. The car has a mass m and is experiencing a force F from the push. However all forces need to be taken into account for this kind of calculation: the car also experiences a force, let us call it X, which is acting in the opposite direction: friction, which is familiar from everyday life. To calculate the acceleration of the car, first rearrange the equation algebraically to make the required quantity, a, the subject:
F = ma becomes a = F / m
Now substitute in the total force being applied to the toy car, also called the net force. This is the sum of all forces being applied, taking into account their directions. For the toy car, this is X (the friction force) subtracted from F (the push force). Algebraically this can be expressed as
a = (F – X) / m
The Vector Approach
Another way to perform this calculation is to use a more mathematically based vector approach of taking the direction of the push as the “positive” direction thus meaning the net force is F plus –X which is equivalent mathematically to F - X anyway. This may seem like unnecessary extra work for a simple case such as the toy car, but is an essential methodology for more complex problems which may feature many forces and force components acting in multiple directions on an object.
Reference
"Newton's Laws of Motion," online at NASA's Glenn Research Centre; Beginner's Guides Grc.nasa.gov Accessed May 2010
