



I will now make a bold statement: everyone has an intuitive understanding of how motion works! Don't believe me? let's just take the example of crossing the road, you look left and right, see if there are any cars coming your way and you are able to intuitively calculate whether it is safe or not cross the road at that time, insane right?





but what if we had numbers... what if we could quantify 'speed' and the rate o'change of speed 'acceleration' ....? would there even be a use to this endeavor ? great questions which I'll try to answer





1.Position and it's related quantities





If you had some point in space, you could measure the distance of another points in terms of the x,y,z coordinates ( vertical, horizontal and whatever z-axis is called) relative to that point. For the sake of simplicity and the precious time , let us approximate our object of interest as a point. Usually the point we take is a special one known as the center of mass.





Now say you move as time changes, then you then rate at which the position variables change with time, would be defined as your velocity. A simple ratio of change in position over change in time, the most general way to speak of this is using derivatives but we wont go in that depth right now.

Dont get lost in the space tho

The total velocity of you moving through space would be the combination of the velocities along each direction working at once. ( Now if you are smart and you know vectors....)





Now most of the time velocity is not always a constant parameter, that is, it changes with time, say you move in a gravitational field, You move faster and faster the more you stay in that field (if you are not constrained to any place). The rate of change of velocity is known as acceleration.

my g



2. Newtons Great Idea



Now the next natural thing to tackle is dynamics of how two bodies interact and some general results we can get on all sorts of motions. Newton did us a nice work by summarizing almost all of classical physics into three laws.



Law-1: Inertia



A body stays in it's state of motion and can only change it's motion if and only if acted by a unbalanced force



The simple understanding of this law is that you cant have a sudden shifts in how you are moving without a reasoning (Force) . There should be some sort of force responsible for any type of change in motion. That means you will not suddenly with no reason go from rest to motion and vice versa.



I would say this is a very intuitive law, as the opposite statement sounds nonsensical. " you can have sudden shifts in your motion" , that would make the world really random. This doesn't imply that we can have really unstable and random sorts of motion, actually, these exist. Search up "Brownian motion" for more about that.



Error: TOo much motion



Law-2 : F=ma



The fundamental equation from which we can have a quantitative study of physics. It basically states that the total sum force one a body is mass * acceleration. Now a natural question would be "what is a force?" I could give you a definition but that wouldn't capture the true meaning behind so bear with me for a while ( For the time being think of it no more than an equation)



To practically use this equation simply find all the forces acting on the point particle and equate it to ma,Now usually what you get is known as a second degree differential equation, if you are able to solve this differential equation, you will be able to find a relation which associates each points in time to the position of the particle at that time.





So using this relation we would be able to say where our particle would be at the next second, the next minute, the next hour and so on and so forth.



Law 3: Action Reaction





Now finally I can tell you why we talk of forces instead of just saying acceleration!



So lets say two bodies collide, it is not necessary that two bodies would have the same acceleration after collision that is just silly. Imagine hitting a ball with a baseball, if both objects had same acceleration, the bat and the baseballer would fly away in the exact opposite direction given he is still holding on to the bat.



I think that all of us got an intuitive idea that there should be some quantity that bat must be imparting on this ball and it must be in equal and opposite amounts for both the bat and the ball. And it turns out that this quantity was found to be none other than the force! and that is why we like speaking about it so much, in collisions , the force of one body on another is equal to the force of another on the body but in the opposite direction.







This 'view' of forces also works in the statics case, let us say you sit on a chair, then the base of the chair which you sit on is providing a force to oppose your weight. If it didn't then the chair would compress like a sponge would when you sit on it.





Now the next natural thing to tackle is dynamics of how two bodies interact and some general results we can get on all sorts of motions. Newton did us a nice work by summarizing almost all of classical physics into three laws.A body stays in it's state of motion and can only change it's motion if and only if acted by a unbalanced forceThe simple understanding of this law is that you cant have a sudden shifts in how you are moving without a reasoning (Force) . There should be some sort of force responsible for any type of change in motion. That means you will not suddenly with no reason go from rest to motion and vice versa.I would say this is a very intuitive law, as the opposite statement sounds nonsensical. " you can have sudden shifts in your motion" , that would make the world really random. This doesn't imply that we can have really unstable and random sorts of motion, actually, these exist. Search up "Brownian motion" for more about that.The fundamental equation from which we can have a quantitative study of physics. It basically states that the total sum force one a body is mass * acceleration. Now a natural question would be "what is a force?" I could give you a definition but that wouldn't capture the true meaning behind so bear with me for a while ( For the time being think of it no more than an equation)To practically use this equation simply find all the forces acting on the point particle and equate it to ma,Now usually what you get is known as a second degree differential equation, if you are able to solve this differential equation, you will be able to find a relation which associates each points in time to the position of the particle at that time.So using this relation we would be able to say where our particle would be at the next second, the next minute, the next hour and so on and so forth.Now finally I can tell you why we talk of forces instead of just saying acceleration!So lets say two bodies collide, it is not necessary that two bodies would have the same acceleration after collision that is just silly. Imagine hitting a ball with a baseball, if both objects had same acceleration, the bat and the baseballer would fly away in the exact opposite direction given he is still holding on to the bat.I think that all of us got an intuitive idea that there should be some quantity that bat must be imparting on this ball and it must be in equal and opposite amounts for both the bat and the ball. And it turns out that this quantity was found to be none other than the force! and that is why we like speaking about it so much, in collisions , the force of one body on another is equal to the force of another on the body but in the opposite direction.This 'view' of forces also works in the statics case, let us say you sit on a chair, then the base of the chair which you sit on is providing a force to oppose your weight. If it didn't then the chair would compress like a sponge would when you sit on it.

Now I'll do a slight bit of foreshadowing...

Force is not the only quantity which is conserved, there are actually many mores but they are all connected through some integrals and derivatives



3. The point of all this

Well now that we have defined the basic quantities related to motion and spoken about newtons laws, we may ask ourselves the following question: what is the point of all of this? There are many answers to this question but I propose one certain answer.

As I said before we can know where a body will be in the past,present and future using the simple quantities we defined and newton laws. This helps us create a mathematical prediction of how the trajectory of the motion will be given we know the initial conditions ( remember differential eqns?).

The laws are not limited to simple motions, we could also use these laws for modelling natural phenomena such as fluid flow , waves etc.

To summarize: We can model the dynamics of bodies both quantitatively and qualitatively by following some simple principles. Physics is beautiful and Newton is a genius.





To summarize: We can model the dynamics of bodies both quantitatively and qualitatively by following some simple principles. Physics is beautiful and Newton is a genius.









What does it 'mean' to understand motion? an object can move right and left, up and down, in and out of our view, I mean it doesn't sound that complicated or is it?