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Newton's second law review

Review the key concepts, equations, and skills for Newton's second law of motion, including how to analyze motion in the x- and y-directions independently.

Key terms

Term (symbol)Meaning
ΣThe Greek capital letter sigma. It means “sum of” or “adding up all of.”
ΣFThe sum of the forces. Also written as Fnet.
AccelerationThe rate of change of velocity per given unit of time. An object is accelerating if its velocity is changing.
SystemThe collection of objects that are of interest in a problem. Systems can be closed or open, and they can be isolated or not isolated.
EquilibriumThe forces in a system are balanced. When Fnet=0, the system is not accelerating, and velocity is constant. Velocity is zero when a system is in static equilibrium and velocity is constant and non-zero when a system is in dynamic equilibrium.


EquationSymbol breakdownMeaning in words
a=ΣFm=Fnetma is acceleration, ΣF is the net external force, and m is mass of the system.Acceleration is the net force divided by the mass of the system.

Newton’s second law of motion

Newton’s second law says that the acceleration and net external force are directly proportional, and there is an inversely proportional relationship between acceleration and mass. For example, a large force on a tiny object gives it a huge acceleration, but a small force on a huge object gives it very little acceleration. Also, force and acceleration are in the same direction.
The equation for Newton's second law is:
We can also rearrange the equation to solve for net force:
Where a is acceleration, ΣF is the net external force, and m is mass of the system.

Solving problems using Newton’s second law

To use Newton's second law, we draw a free body diagram to identify all the forces and their directions. It is helpful to align our coordinate system so that the direction of acceleration is parallel to one of our axes.
The x- and y-directions are perpendicular and are analyzed independently. In other words, for the x-direction we can write:
And for the y-direction we can write:
Newton’s second law equation can be rearranged to solve for the unknown mass, acceleration, or force.

What else should I know about Newton’s second law of motion?

  1. Balanced forces can cause the net force of an object to be zero. Multiple forces can act on an object. If the forces are balanced, the net force is zero and the object’s acceleration is also zero.
  2. There are limitations to Newton’s laws. Newton’s laws are excellent for modeling our experience of the world. When we start investigating objects that are approaching the speed of light or are on the atomic scale, Newton’s laws are no longer accurate. Physicists have had to come up with additional models for these situations.

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