Newton's Era
Fundamental Framework
Present Theories
Exercise
Gallery
 
 
LATEST NEWS
 

The speed of light changed recently - New experiments in Oklo reactor in West Africa have shown that a fundamental constant of the nature (alpha) has changed recently; this consists of the ‘c’ term. So, the speed of light may have changed recently. Visit this site - www.newscientist.com (click here) for further reading.

New form of loop quantum gravity arrives - this new form says that particles are made up of tangles in space. Finally, theory has obtained a generalization of all particles like string theory but without any use of background space. Visit this site - http://www.newscientist.com/article/mg19125642.900.html (click here).

Quantum gravitation states - For the first time, physicists have observed quantum states which are quantized under the effect of the gravitational field. The vertical motion of ultracold neutrons comes in quantized size. Visit this site - http://www.aip.org/pnu/2002/573.html (click here).

Physicists have found ways to see extra dimension - They can now make a model of extra dimensions by studying the pattern of cosmic energy emitted during big bang - a model based on the Superstring theory. Visit this site- http://www.brightsurf.com/news/headlines/28677/Physicists_find_way_to_see_extra_dimensions.html (click here).

Dark matter no longer present - Physicists have developed a new model in which behaviour of gravity becomes a bit different at cosmological level leading to the acceleration of the universe. This model does not need a dark matter presence. Visit this site - http://physicsworld.com/cws/article/news/24139 (click here).

Measurement paradox - A new paper by Prof. Lawrence Krauss (Prof. of Astronomy, Case Western Reserve University) suggests that the observation of dark matter may affect the age of the universe. Visit this site - http://arstechnica.com/news.ars/post/20071125-human-observation-of-dark-energy-may-shorten-the-life-span-of-the-universe.html (click here).

 

LAWS OF MOTION
 
 

LAWS OF MOTION

Newton was a reincarnation of Galileo, a rebirth of Galileo to take his work to greater domains. What Newton did for Science, no one had done till the arrival of Einstein. Newton and Einstein had striking similarities. Both worked on the principle of relativity, on gravitation and both were deeply interested in the nature of light. It is difficult to say who was greater. Both of them brought new ideas to the world. We will first see Newton’s contributions. Next few sections are devoted to his works and their development.
 

The three very famous laws of motion: the law of inertia which states a body’s ability to retain its original state of motion or rest, the second law which defines force as a quantity which brings about a change in momentum, the action-reaction law which says that to every action, there is an equal and opposite reaction, form the fundamentality of any textbook of Physics. The first law is very closely related to Galileo’s experiments on inertia. It more deeply says that a state of rest or of uniform motion is basically the same thing since body can be in either of them. The second law gives a well-working formula for force and says that without force, inertia cannot be changed. The third law makes things very symmetrical. This law is necessary to prevent us from sinking down a table. Newton obtained a very fundamental law describing the motion of a particle:

Acceleration = force/mass = d2r/dt2, where r is the position vector.

Newton’s laws are very consistent with Galilean transformation (Look at Exercise Q.1 of Level 1). So, we do not expect these laws to hold in Einstein’s framework which is a more generalized form of Galilean transformation or Newton’s laws.

Now, let us turn to his law of gravitation. It says that the gravitational force on a body of mass m from a body of mass M acts towards the larger body.

So, F = -GMm/r2. So, acceleration of the smaller body = -Gm/r2. Now, we will derive Kepler’s laws from this.

 

First, consider a fundamental principle of rotation. If torque does not act on a body, its angular momentum is conserved. Force acts radially; so, its line of action passes through the centre and hence, no torque acts. So, angular momentum is conserved for gravity.

Angular momentum is defined in scalar form as L=mvr. You can easily understand what these symbols mean.
Now, v = wr (w is angular velocity)
w = dq / dt.

Therefore, mr2(dq/dt)=L0 (L0 is a constant initial angular momentum)
            => r2(dq /dt)=k (k = L0 / m)                                …………..(1)

1   2   3
GALILEO’S INSIGHTS
 
 
 

Site designed by Warpsters