SCIENCE CAPSULES

         We know the conservation of energy, mass, and momentum are cornerstones of science.  We have studied the 'Law of conservation of angular momentum' in school physics.  It also holds some surprising facts.  We will see them now.      Momentum is the product of mass and velocity.  Angular momentum is the product of the 'moment of inertia' and angular velocity.  The moment of inertia plays the role of mass in a circular motion.  It is roughly the product of rotating mass and its distance from the axis of rotation. Hence Angular momentum = Moment of inertia* angular velocity = constant or Mass * distance from axis*angular velocity = constant   In the above formula, if one quantity increases, another quantity must decrease to keep the product constant.     A dancer on an ordinary floor or ice floor sometimes spins herself.  If she out-stretches her arms, she will spin slowly....

         How they measure chance? what are the basic operations in probability? Let us find out.       In tossing of a coin, there are two events-- head and tail.  The chance one event occurring = one/total number of events.  That is 1/2.  You have 50% chance of getting head or tail for each toss.  If you toss a coin, one time you should get head and next time you should get tail, so the formula says.  But both the times, you may get head or tail.  If you toss the coin 100 times, roughly 50 times you will get head and tail.  On the long run, the formula proves correct.     On throwing dice, there are six events (1,2,3,4,5,6).  Hence chance of getting an 'event' for a throw is 1/6.  There are three important logical operations in probability.  Let us go for it.   OR operation:     What is the chance or probability getting 1 or 6 in a roll.  Here, either 1 or 6...

1. Add two numbers        2+2 = 4 2. Add the number repeatedly      4+4 +4 = 12   3*4 = 12 That is multiplication 3. Now multiply repeatedly       12*12*12 = 1728  12ˆ3 = 1728     That is taking power     Let us go backwards. 1. Take cube root of 1728, we get 12                      (dividing repeatedly) 2. Divide 12 by 3, we get 4                         (subtracting repeatedly) 3. Subtract 2 from 4, we get 2  Addition is the basic operation, in moving forward.  But subtraction is the basic operation when moving backward.      Using addition and subtraction, we can move to and fro in mathematical process and get the desired answers. Calculus designed in similar fashion.     As an example consider a freely falling body.  We kno...

         Whenever we wait for the city buses, they do not turn up for a long time or they come in groups of 3 or 4.  Why this happens?   Say, buses in a particular route are scheduled to arrive at a 'stop' for every 12 minutes.  That is, 5 buses are expected in a bus-stop in an hour.  But they are bunched up or scattered away due to heavy traffic or other odd reasons.  But there is a statistical formula (exponential distribution) using which, we can calculate our 'chance' of getting  a bus in an interval of time.       P = 1-eˆ(-rk) P- probability or chance of occurrence of event in the interval of time 0 sec to k second.     e- 2.71 ... Euler's constant.     r - rate of occurrence of events  In our case;  k = 5 minutes  r = 1/12:   one bus arrives for every 12 minutes. or 1/12 of a bus arrives at every minute. Now p = 1- 2.71 ˆ[-5(1/12)]     ...

          If you toss a coin 5 times, 4 times you may get head and one time you may get tail.  Toss it 10 times, it may be head 7 times or 3 times tail.  Toss it 100 times. Roughly 50 times you will get head or tail.  If you do 10000 times, Most likely 5000 times we get head or tail.  A computer can easily simulate this process.  As the 'number' increases, we reach the fifty percent probability. 7/10 is not 50%  But 5007/10000 is.      Let us roll the dice three times, it may be 2,4,6.  The average is 2+4+6/3 =4.  But, if we roll the dice many, many times and find the average, it will settle down exactly at 3.5.   1,1,2,3,5,8,13....144,233....      The above is the Fibonacci series, Adding the previous two numbers, you get the next number.  Now take successive numbers one by one and find their ratio.     2/1 = 2     3/2 = 1.5     5/3 = 1.666 ...

       In a land line, voice is converted into electrical signals by a microphone and sent through wire.  The sound is reproduced by the speaker at the other end.  Now we have modern technology called fiber optics.  Here voice or digital data is first converted into electrical signals and then into light signals(laser or infra red) using electronic element.  It is then sent through glass fibers (strands).      We know, electric current flows through metal wire because electrons are pulled by voltage difference.  But how the light will travel through glass fibers without oozing out?  Imagine long narrow hall way.  Its walls fitted with mirrors.  Hallway goes zig-zag.  If you send a torch light beam to a mirrored wall, it will reflect and re-reflect on the walls again and again and travel trough the hallway.  Similarly, laser beam travels through glass strands using 'total internal reflections'. ...

CLASS V Student A :  What is the boiling point of water? Teacher:      100 degree c is said to be the boiling point of water. Student A:   Why 100 degree c ? Teacher:  At 100 degree c , water bubbles up and evaporates. Student A:  O.K. CLASS X Student B:  What is really happening at the boiling point? Teacher:  Liquid water changes into gaseous state.  At the boiling point, the water molecules gains enough energy to flight the air molecules and escapes into the atmosphere.  Hence at 100 degree c, the water vapour pressure and the atmospheric pressure equals. CLASS XII  Student C:  What you mean by 'liquid changes into gas'? Teacher:  The water molecules has positive end and the negative end.  The positive side of one molecule attracts negative side of another molecule.  Hence the water molecules cling together as a drop, as a liquid.  As the temperature increases, the molecules gai...