If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Newton's second law review

NGSS.HS:
HS‑PS2‑1
,
HS‑PS2.A.1
,
HS‑PS2.A
,
HS‑PS2
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
\SigmaThe Greek capital letter sigma. It means “sum of” or “adding up all of.”
\Sigma, F, with, vector, on topThe sum of the forces. Also written as F, with, vector, on top, start subscript, start text, n, e, t, end text, end subscript.
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 F, with, vector, on top, start subscript, start text, n, e, t, end text, end subscript, equals, 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.

Equations

EquationSymbol breakdownMeaning in words
a, with, vector, on top, equals, start fraction, \Sigma, F, with, vector, on top, divided by, m, end fraction, equals, start fraction, F, with, vector, on top, start subscript, start text, n, e, t, end text, end subscript, divided by, m, end fractiona, with, vector, on top is acceleration, \Sigma, F, with, vector, on top 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:
a, with, vector, on top, equals, start fraction, \Sigma, F, with, vector, on top, divided by, m, end fraction, equals, start fraction, F, with, vector, on top, start subscript, start text, n, e, t, end text, end subscript, divided by, m, end fraction
We can also rearrange the equation to solve for net force:
\Sigma, F, with, vector, on top, equals, m, a, with, vector, on top
Where a, with, vector, on top is acceleration, \Sigma, F, with, vector, on top 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:
\Sigma, F, with, vector, on top, start subscript, x, end subscript, equals, m, a, with, vector, on top, start subscript, x, end subscript
And for the y-direction we can write:
\Sigma, F, with, vector, on top, start subscript, y, end subscript, equals, m, a, with, vector, on top, start subscript, y, end subscript
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?
    (9 votes)
    Default Khan Academy avatar avatar for user
    • 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.
      (6 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?
    (4 votes)
    Default Khan Academy avatar avatar for user
    • 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.
      (5 votes)
  • starky tree style avatar for user Davïd
    This is some yummy brain food!
    Nom nOm noM.
    (5 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Salam Lababidi
    hello, please I would like to know when is the acceleration considered to be negative?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • primosaur tree style avatar for user Rukaiya
    Is it possible a body can be in motion without any force?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user 1khaldiwafa
    Equilibrium The forces are balanced, so net F equals 0 and the system is not accelerating. Velocity can be non-zero. i have not really undrstood the state of the velocity.
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user aqeelah1995
    Can you cover the topic of balancing objects or equilibrium?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user iceberg
    I don't understand exactly how an object with constant velocity that isn't at rest has a resultant force of zero, is there always some kind of opposing force? But what if there isn't a force such as friction or air resistance? I'm confused
    (1 vote)
    Default Khan Academy avatar avatar for user
    • cacteye green style avatar for user pa_u_los
      Acceleration implies force. If we have constant velocity that means that we don't have acceleration. If we don't have an acceleration, that means that there's no force involved.

      In real life, yes. If we only focus on classical mechanics and not the physics behind it that explains more profoundly why it works like that, I can't think of any force that doesn't have an opposing force. Every material has an associate coefficient of friction. If there's no force such as friction or air resistance, objects would experience a constant acceleration, meaning they would be speeding up until reaching the speed of light all the time. Because if we are at a rest (0 velocity) and want to change our velocity we need a force. And that force wouldn't had a counterpart. We would be constantly accelerating, making life pretty difficult. If not, not viable.
      (3 votes)
  • boggle yellow style avatar for user Zoe LeVell
    If the sum of the forces and acceleration always point in the same direction, but forces can never be negative, then how can acceleration be negative?
    (1 vote)
    Default Khan Academy avatar avatar for user
    • eggleston blue style avatar for user IsotonicFlaccidCell21
      Forces can be negative. Forces are vectors. Here is an example:
      you are pushing a box with a force of 5N. However, friction with the ground is pushing bat with a force of 2N. Hence, if you were to add all the forces it would be 5 + (-2) =3. This is because the 2N is acting in the opposite direction, hence it is negative.
      For your second part (how acceleration can be negative):
      let's say you are at terminal velocity (Constant velocity) in the air and you are falling. Your weight is (let's say) 700N. You suddenly open up your parachute, causing air resistance, pushing you up with a force of 1000N. As going down is a positive force, the resultant force would be 700 + (-1000) = -300N. Here you have a negative force going downwards, meaning that you are decelerating (retarding). This is how acceleration is negative. As the force is negative, and your mass is constant and positive, that means your acceleration downwards must be negative. Thus you will slow down.
      (1 vote)
  • blobby green style avatar for user lbarbour24
    How can you calculate the motion of acceleration?
    (1 vote)
    Default Khan Academy avatar avatar for user