THE STROBOSCOPIC EFFECT

When a running fan is viewed under tube light, it appears to rotate backwards or forwards.

Our houses are supplied with alternating current of frequency 50 cycles per second. That means, the current is 'on' for 50 times a second and 'off' 50 times a second.

Our eyes has the property called 'persistence of vision'. It means, whenever we see an object, it's image is retained in the eye for one tenth of a second. No image in the eye vanish immediately. Due to this property, our eyes do not perceive flickering of the electrical lamp which arises because of alternating current.

Say, now you are viewing a table fan under electrical lamp. When light (current) is 'on', a particular image of the fan blade is recorded in our eyes. When the lamp is 'off' for some milli- seconds, the fan blade might have rotated by an angle to a new position. The new position of the blade may be in forward or backward to the original position depending on the speed of the fan. When the light comes, our eyes see the new position of the blade and perceive it as rotating forward or backward. This is called stroboscopic effect.

Note 1. This effect does not occur in natural light source like sun and candle which emit light continuously.

Note 2. When a fan is running at the speed of 50 rotations per second, it appears to be stationary under electrical lamp. If the speed is different from 50 rps, the blades appears to rotate slowly forwards or backwards depending on the speed.

So the fan and lamp teach you 1. alternating current 2. frequency 3. persistence of vision which is made use in the making of the movies. 4. rotation speed 5. relative speed and 6. illusion.

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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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