Again at first glance this looks very simple but because there are so many
forces acting around us all the time, it is easy to get this all mixed up.
We often like to state Newton's Second Law as F=ma but the correct
form (the form that Newton described) is a=F/m. This is a "correct"
form because acceleration is caused by the force and the mass. In the
typical form one might be convinced that force is caused by mass and acceleration
which leads to many incorrect conclusions.

In this simple equation, force and acceleration are both vectors, meaning
they both have a defined direction and they must be in the **same **direction.
In addition, the force and acceleration must be from the same cause.
Example, using the acceleration of gravity to determine the force
of a car engine does not work. Mass in this equation is scalar, meaning
that it is direction independent. You can push (force) something north,
but it doesn't make sense to suggset that 15 Kg is north.

When the acceleration is being measured (as in a=(v_{f} - v_{i}
)/t for example) the acceleration is caused by the **net force.** The
net force is the sum of all the forces. Because forces can act in
different directions at the same time it is often useful to separate the
components before doing any calculations. Add to these components
the fact that there is usually more than one force many students get "lost"
in the calculations if each part is not carefully considered and included
in the determination of the net force. One technique that helps keep
track of all of these forces is called a Free Body Diagram (FBD) or a Force
Diagram. We will get plenty of practice with these diagrams in class.

One very common mistake in considering forces is the confusion of mass
and weight. Mass is a measure of inertia, the amount of matter in
an object, the resistance to the change in motion. Weight is simply
the force of gravity. Mass does not have direction, weight has a direction
of down (usually we designate this as the negative y direction). Mass
is measured in kilograms or slugs, weight in newtons or pounds. Because
the acceleration of gravity near the surface of the earth is so constant
(9.8 m/s^{2} or 32 ft/s^{2}) it is easy to calculate the
weight (F=ma) if the mass is known or to calculate the mass if the weight
is known (m=F/a). Even thought it is "easy" to do, it is a concept
that is difficult for most students to "get".

The Physics Classroom - Free Body Diagams and More!

Free Body Diagrams from WWU

From UNM

From Integrated Publishing

Interactive practice problems from U of Penn

Simple directions from Univ Utah

Find additional links yourself! Search for "free body diagrams", "uniform circular motion", "Newton's Second Law" or even force + rollercoaster.