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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.]

Want to join the conversation?

  • blobby green style avatar for user Elan Fayngersh
    The videos on Newton Second Law of Motion only showed things in their current state; how would you show something moving, for example, accelerating North at 20 Newtons and slowing down by a Southern moving force of 15 Newtons. How would that be shown in an illustration like the ones in the video?
    (16 votes)
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    • marcimus purple style avatar for user Fiona T
      If you wanted to illustrate the object in a free body diagram, you would just draw the forces acting on it, as in the example you gave with 20N north and 15N south (similarly to how the objects were shown in the video). The object's velocity and acceleration are not included as part of a free body diagram, but I usually notate those as arrows on the side for visual convenience.
      (11 votes)
  • piceratops ultimate style avatar for user Danlearning
    Hi! I'm wondering why the velocity could be non-zero when the forces are at equilibrium (F_net=0) and when the acceleration is also 0. Shouldn't velocity only be 0 (according to Newton's First Law) because the forces are balanced and acceleration doesn't exist?
    (6 votes)
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    • duskpin ultimate style avatar for user BeeGee
      Okay, I'm going to remind you of some things you already know: acceleration can be defined as the change in velocity over time, and if a force is being applied to something it should accelerate unless an equal and opposite force is being applied. (An equal force is being applied in the direction opposite of the original force)
      If an object is moving, and there are no forces being applied to is (no friction, gravity, or any work whatsoever) then it is not accelerating, as a force is necessary for acceleration to be observed, and at the same time there are no forces, so F_net=0.
      Okay, you say, but what if there are forces?
      The same principle- as you know F_net=F_1+F_2+...+F_n, so if I were pushing a box along a plane with friction, applying a force of 10 N, and the friction on the box was 10 N in the opposite direction, we would say that the net force is zero, F_net=0, which means there is ALSO no acceleration, even though the box is moving, which means there is a velocity.
      (12 votes)
  • primosaur ultimate style avatar for user peely
    The videos and this article cover the method for 2 and 3 dimensions but what happens in higher dimensions. Are Newton's laws applicable?
    (6 votes)
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  • primosaur tree style avatar for user Rukaiya
    Is it possible a body can be in motion without any force?
    (7 votes)
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  • blobby green style avatar for user dhiemstra
    Is a light particle/wave at equilibrium: acceleration =zero?
    (4 votes)
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  • aqualine ultimate style avatar for user Salam Lababidi
    hello, please I would like to know when is the acceleration considered to be negative?
    (1 vote)
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  • duskpin seedling style avatar for user janiyah.pinckney0381
    Hi, I'm new here and I want to know how to draw a free-body diagram. Does it include the use of the formula as well?
    (3 votes)
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  • starky sapling style avatar for user Arden
    Negative and positive work for backwards and forwards, but what do we do for situations with more than two directions, for example North, South, East and West? If North and South are positive and negative, what are East and West? Or do we use a completely different system?
    (2 votes)
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  • duskpin ultimate style avatar for user Jons9
    What is the difference between inertia and equilibrium?
    (2 votes)
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    • blobby green style avatar for user noahhickey72
      equilibrium is when there is a net force of zero, so the forces acting upon the object equal zero but the velocity is still constant and non-zero. If velocity were zero then it would be static equilibrium. Inertia is a force that acts as a guidline to objects, it keeps them in uniform motion or rest, what makes this different from equilibrium is that when an object is acted upon by an outside force an object still has inertia because objects always have a resistence to change their motion.
      (4 votes)
  • blobby green style avatar for user ramon89463
    what am i looking at
    (3 votes)
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