WHY WE USE 'ROTATIONS' EVERYWHERE?

In this world, rotations are more common than the linear motion. The planets revolves and spins; the electron circles; the wheels roll; the motor and the engine runs; even opening and closing a door is a partial rotation.

Force required : Newton says that if a body is given a push, it will only move in a straight line. Hence, to keep the body in rotation, a force must act and it should act continuously. A force must act from the moving body towards the center ceaselessly. It is centripetal force.
The sun keeps all the nine planets revolving around itself because of gravitational pull which acts as centripetal force.
The electron keeps circling the nucleus because of electrical force of attraction. The electrical motor works because of magnetic Lorentz force.

The moment: Next, take a DVD. Put one ink dot near the center and another ink dot near the edge. Rotate it. You can observe that the dot near the center moves fast and dot at the edge moves less fast. Hence, distance from the center or axis of rotation plays very important role in rotatory motion. This 'distance' is always multiplied with quantities like mass, velocity, momentum, force, inertia in rotating particles and bodies. Multiplying with 'distance' is known as finding 'moment' in physics.
Consider a large carriage door. If you push it at the edge you can easily close and open. But, if you push it near the joint (axis of rotation), it is even difficult to move the door a bit. That is why we find the 'moment of force' to get the real effect of the force.

Stability: Rotating wheels keeps its axis of rotation stable. Examples: spinning top, two wheeler, cycle, the toy-fidget spinner. When they are in motion, they cannot be brought to the ground easily(gyroscope effect)

Energy store: A rotating giant wheel cannot be stopped 'all of a sudden' due to rotational inertia. It will continue to rotate for some time. So a rotating heavy wheel act like mechanical battery storing mechanical energy. This concept is widely used in automobiles.

Compactness: Rotation is a compact motion. It can be contained in an atom; in a motor assembly; in a car; in a DVD player; in a cyclotron; in a gyroscope and so on. Today, people even go for a nano molecular motors. Hence go for rotation always.

Note: Electricity is generated mainly using rotations. Because rotations are easy to execute.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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