**Title of the Paper:**

On Rajankikants 4

^{th}Law of Motion.

**Authors:**

Chinmay Datar 1.

**Special Thanks:**

Taniya Bapat 2.

**Abstract:**

The paper is written with a view of calculating the Rajani Radius(Rajanitrijjya) based on Rajanikants 4

^{th}Law of Motion. The Law itself deals with the movements of superheroes such as Rajinikanth and Flash amongst others. The Law, and its following derivations should not be attempted by normal mortal human beings such as ourselves, for the force that would be exerted is beyond the biological capacity that the body is designed to handle. Superhumans (Heroes) with modified DNA and Superpowerful(and as of yet undiscovered) subatomic particles are the only things to whom the law may apply . The inspiration for this research was provided by a Taniya Bapat SMS forward, for which the author duly recognizes her inputs.

**Index Terms:**

Rajinikanth, Rajanitrijjya, Highspeed circular motion, 4

^{th}Law of Motion, Persistence of vision.

**Introduction:**

Newton is credited to have formulated the first three laws of motion on which the whole universe is based. Well, the whole universe follows these laws except for some nutcases termed as superheroes (Rajani, Flash, Green Lantern, Superman, etc). To fit these heroes’ deeds scientifically, Rajani, the great, came up with a new Law- one that shook the earth beneath the feet of Shri Shri Isaac Newton.

Rajani states in his 4

^{th}Law:**“If you run at 100 km/sec around a tree, you can see your own back”**[1]While physically, it may seem impossible that this can be true, scientifically and mathematically it is quite possible. 100km/s roughly equals 100000m/sec, which is about 0.0003333 times the speed of light, and hence, speed which can be easily achieved by fast things, such as superheroes. This rules out the problem that heroes would need to travel faster than light. Also as the speed is quite fractional and nominal compared to the speed of light "c", relativistic effects and Lorentzian transformations can be ignored.

**On Persistence of Vision and field vision of a human eye:**

An important concept in this derivation is that of “Persistence of Vision”. Our eyes, for a short duration, store the image that it catches on its retina. The effect lasts for a very short time, however, if a body moves at that rate, it appears to our eyes that the object is in continuum. An application for the same is the television, where about 25 frames per second and shown so that the picture appears continuous. From here we can calculate that per frame, 1/25 second is needed for it to be stored on the retina. i.e if the eye sees something even for a minuscule period of time, due to persistence of vision our mind “reads it” for 1/25

^{th}of a second.The second important concept is field of vision. Looking forward, humans usually have a field vision of 95 degrees as shown in the fig below:

**Calculation of the Rajanitrijjya.**

(Trijjya, Sanskrit for Radius) Rajanitrijjya, literally, the Rajani radius is the maximum radius that can be used by a superhero to run in a circle to see his own back. Certain assumptions about speed and radius were made to achieve the results.

Rajani 4 says that you need to run at 100km/sec which gives a speed of 100000m/s. The velocity will be linear velocity. V=100km/s. ω would be v/r, and will depend on the radius.

**Scenario 1**:

**The superhero only sees forward, and has no field of vision while running:**

In this case, the superhero need to be at the same spot that he started from in (1/25) of a second. Only then, will he be able to see his own back.

The distance covered by the superhero would be equal to the circumference of the circle on which he is running.

Thus, we have,

D= s*t;

2*π*r = 100,000 (m/s) *(1/25)(s)

2* π *r= 4000m;

r= 4000m/(2* π);

r= 636.66 m, which is roughly 637 m.

However this will be true only if the Superhuman only looks straight ahead.

**Scenario 2:**

**The superhero possesses a human field of vision**

The superhuman, at the end of the day is a human, and thus, possesses a field of vision, which Wikipedia states is 95 degrees.

Using this, the human may be able to see his back at a position which is not at the exact same spot on the circle from where he started running, but rather on a point much earlier to that.

A quick glance at the following circle will help answer our doubts.

Total field vision is 95 degrees. Assuming symmetry, and assuming the superhero is not cross-eyed (rather doubt it) field of vision per side along the line of symmetry will be: 95/2 = 47.5 degrees.

At any point on the circle, the superhero is running tangentially to the radius at that point. He thus makes an angle of 47.5 degrees with the point from where he started (A) from a point say B. this means that the angle between the furthest vision and the radius is 42.5 degrees. Reminding the reader that the circle has a constant radius (Polar r=a), an isosceles triangle will be formed, subtaining an angle of 95 degrees on the center.

Thus, the superhero would need to run a distance equal to the arc length equivalent to 265 degrees.

Thus, distance covered will be:

(265/360)*2* π *r.

This will be equal to s*t

(265/360)*2* π *r = 100000*1/25

(265/360)*2* π *r= 4000;

R= 4000 *360/(265*2* π)

r= 864.8 m.

Thus if the superhero runs at a radius of roughly 865 m from the centre of the tree, he should be able to see his back.

Now, the widest tree has a diameter of 32 m(from wiki). Thus, radius is 16m. For his own safety, let the superhero run around the tree at a distance of 20m.

Thus,

(265/360)*2* π *20 = s* (1/25)

Thus, s= 2312.5 m/s.

This equals 2.3125km/s

This is just the 1/50

^{th}the speed at which Rajani can run. No wonder he easily sees his own back!Superhumans having such capabilities have been discovered. The wait is for the discovery of the fundamental units that build up these superhumans. These fundamental particles, although as of now only imaginary have been assigned the term Rajanions by VERN (Vadheev Engineers Research Network)- the Research branch of IVEE.

**References:**

[1] SMS, received on 14

^{th }Sept, [Taniya Bapat].

**Acknowledgements:**

The author would thoroughly like to thank Taniya Bapat- still a student for inducing a thought process to formulate the concept of seeing your own back while running.

All material is copyrighted to the IVEE. Any person imitating any research or stealing it (especially non-members) and using it for ridicule, will be given 50 whiplashes. The author or for that matter anyone at IVEE shall not entertain questions regarding how Rajanikant reaches speeds of 100km/s- Go ask Rajanikant himself.

People wishing to promote fun side of Science and Math can contact IVEE chairmen-

**Chinmay Datar**or**Sumedh Dhabu**to obtain and a lease to use the vadheev proofs.
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