Clockclocle said:
I'm stuck to understand 3 laws of Newton. It doesn't make sense to me.
1. Suppose the case when a person stay in a rest vehicle.When we accelerate the car the person still at rest so the person has to move to the tail of the vehicle cause his intertia of staying rest. If we decrese the acceleration to negative immediately, does it give the person a velocity? Cause he move to the head of the car and the car tend to stop.
First of all it is very important to be clear about the fact that there's no absolute space, although that's what Newton proposed, but in this case Leibniz was right. First of all you need a spacetime model and a definition of a frame of reference. In Newtonian mechanics you postulate an absolute time, i.e., the existence of clocks that tick at the same rate, no matter, what happens to them (that's an idealization of course, but the best such clock are the atomic clocks used today to define the unit of time, second, in the SI unit system; maybe not too long from now there'll be even more robust nuclear clocks). Further it is assumed that space is always described as the usual Euclidean space you are used to from your math classes in school. So a reference frame can be simply constructed by using three rigid rods, defining a Cartesian basis system and a reference point, against which you can measure positions of material points and describe there motion as a function of time, as measured by an ideal clock, relative to the so defined reference frame.
Concerning Newtonian dynamics, everything starts with the 1st postulate, which in modern terms simply says that there exist inertial frames of reference, where a particle stays at rest or in rectilinear uniform motion, if it is not interacting with any other particles. In other words, relative to an inertial frame of reference the velocity of a particle, which doesn't interact with anything else, stays constant.
Whether or not a given reference frame is an inertial frame can only be established by observation. Usually we just use a reference frame at rest relative to the Earth and take into account that there's the gravitational interaction of the bodies under investigation due to the gravitational field of the Earth. This seems to be an inertial frame of reference to a not too bad approximation. On the other hand, it's clear that it is unlikely that the Earth, which is rotating around its axis (relative to a reference frame, defined by the fixed stars) to define precisely an inertial frame, and indeed as the famous Foucault-pendulum demonstration shows, the Earth-rest frame is indeed not exactly an inertial frame of reference. The rest frame of the fixed stars turns out to be a better one. The best inertial frame we have is the rest frame of the cosmic microwave background.
Having established an inertial reference frame (with a precision sufficient for the purposes of your application), you can turn to Newton's 2nd Law, which defines mass and force in a quasi-axiomatic way: Mass is a measure for "inertia", i.e., it describes how much "effort" it takes to change the velocity of a body. Newton defined it as being proportional to the "amount of matter", i.e., the mass of a body of a given material twice as large as another of the same material should be twice as large too. Given that measure for inertia, the acceleration of the body depends on the applied force according to ##\vec{F}=m\vec{a}##.
Finally there's Newton's 3rd Law, which deals with a very general property of interactions, i.e., forces acting between several bodies. The most simple case are socalled two-body forces, an that's also the only kind of forces Newton indeed considers. The 3rd Law then says that, if there are two bodies, and there's an interaction between these two bodies such that this interaction imposes on particle 1 a force ##\vec{F}_{12}## due to the presence of particle 2, then the interaction imposes on particle 2 a force ##\vec{F}_{21}## due to the presence of particle 1, and ##\vec{F}_{21}=-\vec{F}_{12}##.
Using these postulates, the other great achievement of Newton, was the general law of the gravitational interaction, i.e., that between two "point-like bodies" there's an interaction force
$$\vec{F}_{12}=-\vec{F}_{21}=-G m_1 m_2 \frac{\vec{x}_1-\vec{x}_2}{|\vec{x}_1-\vec{x}_2|^3},$$
where ##G## is a constant (the Gravitational constant) and ##m_1## and ##m_2## are the masses and ##\vec{r}_1## and ##\vec{r}_2## are the position vectors relative to an arbitrary inertial frame of reference.
Clockclocle said:
2.Does the big intertial cause a big time to change the state of motion? When I push an empty box it seem immediately move but if I push a fullfill box it take a little bit of time to start moving.
3. When I push a book to hit another, why it still move a little bit when the second book applied the same force but negative direction? it should be stop or going backward.
