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Newton's Second Law tells us that $\sum F = ma$. The vector sum of the forces $F$ on an object is equal to the mass $m$ of that object multiplied by the acceleration vector $a$ of the object.

So what is the relation between this law, and the law that says that the sum of all the forces on an object is equal to zero? And what happens if the object has zero velocity?

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There is no law that says the sum of forces on a given object must be $0$, that is simply the condition for mechanical equilibrium.

If an object has constant $0$ velocity (or, more generally, any constant velocity), then its acceleration ($\frac{dv}{dt}$) is $0$ and, by Newton's second law as you have it, the net force acting on it is $0$. However, if all you know is that $v=0$ at some point in time (with no additional information), then you do not have enough information to assess $\frac{dv}{dt}$ and hence cannot draw a conclusion regarding $F_{net}$.

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Just think if there is a law that states that the sum of all forces on an object is zero then there will be no motion in this world or universe. SO there is no such law.

Newton’s second law of motion states that if there are forces acting on a body then the net force (that would be vector sum of all forces) is equal to the product of the mass of the body and the acceleration induced by this net force. Often written as

$$\boldsymbol F_\mathrm{net} = m \boldsymbol a$$

Important to note that the acceleration is a result of force and not vice versa. While tackling problems that utilize Newton’s 2nd law of motion, one should first establish the left side of the equation by taking the vector sum of all forces and then equate with the RHS

The second law is often also stated as -

“The rate of change of momentum of an object is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force”. In the equation $F = ma$, if you write $a$ as $dv/dt$ and take $m$ inside to express it as $F = d(mv)/dt$, what you get is $F =$ rate of change of momentum where $mv$ is momentum of mass $m$.

However, Newton's law does not apply under 2 conditions -

One, if the object is moving at speeds that are close to or comparable with that of light. Under such conditions Einstein’s special theory of relativity explains the motion. Two, the size of the object is atomic - This then falls in the realm of quantum mechanics

You may like to see this video, made by me to understand the law better

NEWTON'S SECOND LAW OF MOTION

enter image description here

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  • $\begingroup$ Please note that if you made those videos, you must say so explicitly in the post. Otherwise your answer (which is nice) would be considered spam. Thanks. $\endgroup$ Dec 28, 2017 at 17:39
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The relation is:

$\sum F=0$ comes from $\sum F=ma$

If $\sum F=0$, so that either $m$ or $a$ must be $0$.

Currently, there is no substance of mass $0$.

So, $a=0$. Means that no force is applied to the object. If it is moving, it will continuously move with constant velocity. If the $v=0$ , the object will stay stationary.

Hope you understand.

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    $\begingroup$ Why vote down? , reason please. $\endgroup$ Apr 6, 2014 at 13:25
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    $\begingroup$ I might understand why someone does not like this answer (although it sounds ok to me), but four down votes? What's the objection? $\endgroup$
    – garyp
    Dec 28, 2017 at 17:36

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