Newton's Second Law equation.  A vector equals the equation sum of eff vector divided by em equals eff net vector divided by em.

Overview of Newton’s Second Law Equation

The Newton’s Second Law equation is used for determining the acceleration of an object of mass m that has a net force acting on it. This net force can be the resultant of multiple other forces.  That’s why there is a sigma in the middle version of the equation.

An example would be a situation where 15 newtons of force are applied to an object with a mass of 3.0 kilograms.  In this case, the object would have an acceleration of 5.0 m/s².  As always, you might be given any two of the three variables.

Variables in the Equation

This equation relates the acceleration, net force, and mass.

a represents the acceleration of the object.

m represents the mass of the object.

There are two ways to represent the force, each equivalent to the other.

Σ F or Fnet represents the sum of the forces on the object.

Notice that both a and F are vectors.  The two vectors point in the same direction.  If there are multiple forces, the individual forces can have several directions, but the acceleration points in the direction of the net force.   

Units in Newton’s Second Law Equation

Newton's Second Law Equation Units.  Acceleration in m/s² equals force in newtons divided by mass in kilograms.

We almost always use this equation with metric units.  

a has units of meters per second squared (m/s²)

m has units of kilograms (kg) 

F has units of newtons (N) or (kg m/s²)

If you are using other groups of variables, you will usually need to convert to m/s², kg, and N.  In situations where very small masses are involved, make sure that you don’t leave the mass in grams, unless you also adjust to millinewtons.

Things to Watch Out for in the Equation

The equation does have vector signs, so make sure that you first find the net force.  For example, if an object is on a level floor, the normal force and the force of gravity are likely to cancel out.  Therefore, only forces in the horizontal direction, like a push and/or friction will cause acceleration.  Friction will act opposite to the forward push on the object, reducing the overall acceleration.

If an object is subject to a force that isn’t all in the same direction as the acceleration, you’ll need to find the component in the direction of the acceleration and only use that part for the problem.

Variations of the Newton’s Second Law Equation

Newton's Second Law Equation.  Sum of eff vector equals em times A vector.

The arrangement of this equation provided on the AP Physics reference sheet is probably the better way to present this equation, as Newton defined the acceleration as resulting from dividing the force by the mass.  However, you will often see this equation presented as…

In this case, the equation has been solved for the force.  Notice that in this version, the definition of the unit newton is apparent. 

Definition of the newton.  One newton equals 1 kilogram times 1 meter per second squared.