# Can I say $F_s=-kx$ is also equals $F=ma$? [closed]

Is $$F=ma$$ a general formula for all cases in the physical world? or Is it only limited in linear motion?

$$F=ma$$ is a general formula. What I mean by general formula is that it is true for both translational ("linear") and rotational motion.

However $$F$$ doesn't correspond to any force acting on a body. It actually refers to the net force acting on the body.
Example: Say a ball is rolling down an inclined plane. $$F$$ corresponds to combination of the gravitational force, reaction force from the surface of the plane, air drag, friction force between the ball and the plane.

In short $$F = ma$$ is a law and defines the outcomes of the interaction with surrounding, whereas $$F = -k x$$ is a function which defines how a force varies with time. For example (say) $$F= 6\ \mathrm N$$ but here too $$F=ma$$ is true and defines how a body would move under the action of a force of given magnitude (here $$6\ \mathrm N$$).

You may also like to look at it with the following perspective:

When we say $$v = \dfrac {\mathrm dx}{\mathrm dt}$$ we mean that at any given instant $$v$$ is defined as the derivative of $$x$$ but it does not say anything about how it varies with time (unless you know what $$x$$ is as a function of time), whereas $$v = a x$$ tells us how the magnitude of $$v$$ varies with time.

$$\vec{F}=m\vec{a}$$ is the general formula. Written in its vectorial form it aplies for translational motion of any kind, not just linear.

Well, The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

If it's written in an equation, then it states: a = sigma F/m

a and F are vectors, meaning that the magnitude and direction can vary, so they don't need to be linear motion