Momentum is an example, and we must define it precisely. If we exert a certain push with our arms on an object that is light, it moves easily; if we push just as hard on another object that is much heavier in the usual sense, then it moves much less rapidly. How hard it is to get it going is one thing, and how much it weighs is something else.

On Mars, weights would be different but the amount of force needed to overcome inertia would be the same. We use the term mass as a quantitative measure of inertia, and we may measure mass, for example, by swinging an object in a circle at a certain speed and measuring how much force we need to keep it in the circle. In this way we find a certain quantity of mass for every object. Now the momentum of an object is a product of two parts: its mass and its velocity.

### Newton's First, Second and Third Laws of Motion

Thus at the beginning we take several things for granted. These ideas were of course implied by Newton when he wrote his equation, for otherwise it is meaningless. For example, suppose the mass varied inversely as the velocity; then the momentum would never change in any circumstance, so the law means nothing unless you know how the mass changes with velocity.

At first we say, it does not change. Then there are some implications concerning force. As a rough approximation we think of force as a kind of push or pull that we make with our muscles, but we can define it more accurately now that we have this law of motion. The most important thing to realize is that this relationship involves not only changes in the magnitude of the momentum or of the velocity but also in their direction.

If the mass is constant, then Eq. Thus we must understand that a change in a velocity, or an acceleration, has a wider meaning than in common language: The velocity of a moving object can change by its speeding up, slowing down when it slows down, we say it accelerates with a negative acceleration , or changing its direction of motion. In order to make our language more precise, we shall make one further definition in our use of the words speed and velocity.

Ordinarily we think of speed and velocity as being the same, and in ordinary language they are the same. But in physics we have taken advantage of the fact that there are two words and have chosen to use them to distinguish two ideas. We carefully distinguish velocity, which has both magnitude and direction, from speed, which we choose to mean the magnitude of the velocity, but which does not include the direction. Suppose, for example, that at a certain instant an object is moving as shown in Fig.

In Eq. Next, suppose that, because of the action of a force, the velocity changes to some other direction and a different magnitude, as shown in Fig. Let us consider a simple example. A falling body moves horizontally without any change in horizontal motion, while it moves vertically the same way as it would move if the horizontal motion were zero. If an object is accelerating, some agency is at work; find it. Our program for the future of dynamics must be to find the laws for the force. Newton himself went on to give some examples. In the case of gravity he gave a specific formula for the force.

In the case of other forces he gave some part of the information in his Third Law, which we will study in the next chapter, having to do with the equality of action and reaction. Again we find that the motion in the horizontal direction is at constant velocity. As another example, let us suppose that we have been able to build a gadget Fig. If we forget about gravity, which is of course balanced out by the initial stretch of the spring, and talk only about excess forces, we see that if we pull the mass down, the spring pulls up, while if we push it up the spring pulls down.

This machine has been designed carefully so that the force is greater, the more we pull it up, in exact proportion to the displacement from the balanced condition, and the force upward is similarly proportional to how far we pull down. Now let us try to analyze just what Eq. If we can answer this question our problem is solved, for then we can start with the given condition and compute how it changes for the first instant, the next instant, the next instant, and so on, and in this way we gradually evolve the motion.

Why does the object move at all? Therefore the velocity which is zero starts to change, because of the law of motion.

Once it starts to build up some velocity the object starts to move up, and so on. Now what about the velocity? And how are we going to find the acceleration?

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That is where the law of dynamics comes in. The law of dynamics tells us what the acceleration is. But Eq. The velocity changes a little bit because of the force, and the position changes a little bit because of the velocity. Now let us really solve the problem.

However, for practical purposes there are some little tricks by which we can increase the accuracy. Then to go through a reasonable total time interval would take a lot of cycles of computation. This can be done if we make a subtle improvement in the technique of the analysis. But the velocity when? The velocity at the beginning of the time interval is one velocity and the velocity at the end of the time interval is another velocity. Our improvement is to use the velocity halfway between.

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## Forces and Newton's laws of motion

If we know the speed now, but the speed is changing, then we are not going to get the right answer by going at the same speed as now. The same considerations also apply to the velocity: to compute the velocity changes, we should use the acceleration midway between the two times at which the velocity is to be found. Now we are ready to carry through our calculation. We just fill in the various spaces in the table one by one. This table now gives us a very good idea of the motion: it starts from rest, first picks up a little upward negative velocity and it loses some of its distance.

But in the weightlessness of orbit, those laws are glaringly obvious - and often very vexing. Russian cosmonaut Yuri Gagarin, during his pioneering first orbit of the Earth in , was the first to experience the practical effects. He put down his pencil while writing his log. Obeying Newton's first law - the same principle of uniform motion that keeps the planets moving around our Sun - the pencil floated out of reach: Gagarin had to complete his log by speaking into a tape recorder.

Nowadays astronauts keep equipment in place with Velcro or bungee straps. Newton's Second Law states that force is needed to accelerate or decelerate a body. In practice this means astronauts must learn how to push themselves carefully through their spacecraft, or else they will simply float around helplessly.

And once astronauts get moving they have to remember to stop themselves as they near where they want to be. Otherwise they'll keep going until they hit something - or someone. First-timers tend to collect a lot of bruises.

## Newtonâ€™s laws of motion | Definition, Examples, & History | pyrmidsgarsay.tk

Some animals flown in space never get the hang of it - one set of new-born quails couldn't adapt to life aboard Russia's Mir space station and died after just a few days. Newton's third law states that for every action there is an equal and opposite reaction. This, too, has very apparent consequences for astronauts: if they so much as try to turn a screw without anchoring themselves to a wall, they'll find themselves twisting instead.