Somersault dive and Change in spacecraft orientation. Two Interesting Applications of Conservation of Angular Momentum.

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     Understanding Physics behind even a simple event give us so much joy and fun.  Here we are going to see two interesting applications of conservation of angular momentum in our real life.

     If you are not aware of conservation of angular momentum, no need to hesitate and hang back.  Just read my blog explaining what is conservation of angular momentum with example and go forward.  Because it will be helpful if you know about torque, angular velocity, rotational inertia.  I have explained in a practical way to make easy to understand. 

Applications of conservation of angular momentum

A Perfect Dive in an Olympic Event

     1.  The springboard diver   Often we have seen, swimmer's somersault dive from a springboard at some height into the water (see the GIF above).  He spins like a ball.  The Physics behind this dive is conservation of angular momentum. 

    

    To make this subject interesting, Imagine, you are a diver now and standing on a spring board at a height of nearly two story building above the deep pool to perform a beautiful somersault dive.  Thrilling right!!! How can you perform such a fantastic somersault dive?  Let us see what to do first.  Just stand on the edge of the board and push the board using your legs with your maximum effort then the board will push you upward. (Caution: while jumping off the board, just be little tilted towards water otherwise you will fall on the same board, don't hurt yourself!!!)  After going up slightly tilted towards water, just tuck your arms and legs closely as shown in the above figure, you no need to take any other effort to spin yourself.  Now you will spin fast and enjoy the somersault dive. Then get into water smoothly other wise you will get hit by water, it is not my fault if you get hit!!!  Follow that Olympic diver.

    We see right from the first In terms of Physics.  When you pushed the board, it pushed you upward with a force so you went up in air.  As you have slightly tilted yourself towards the water, then the force from the board acted on your foot as a torque (turning force) and made you to rotate about your Center of mass.  As you had left the board, you have started rotating in a particular velocity, Angular velocity(⍵).  This angular velocity combined with Rotational Inertia(I) of your body, gave you an Angular Momentum(L).  (Thus angular momentum is L = I x ⍵.  This is similar to linear momentum p = m x v).

    As there was no external torque acting on you in air, the angular momentum cannot change because angular momentum can be changed only by applying an external torque. Then angular momentum is conserved throughout the dive  (like as in linear motion, if a force is not applied, velocity remains the same thus linear momentum will be conserved).  Then how you span fast without any external torque?  Because there was sharing only between rotational inertia and angular velocity.  As you tuck your arms and legs closely the rotational inertia had been decreased, then the angular velocity was increased simultaneously and the total angular momentum of your system remained the same.  This was the simple reason behind the fast spin of a beautiful somersault dive.  That is how the Olympic diver used physics to spin like a ball.

         

    2. Spacecraft orientation     Hope this will be interesting than earlier application.  Because most of us like space and space oriented research or discoveries.  Here you are going to know how satellites, telescopes and spacecrafts changes their direction.  To move them from a place to place relative to earth or any fixed point in a direction,  thruster jets are used.  But just to change their orientation/direction, the principle of conservation of angular momentum is used.

     Usually gyroscopes are used to change the orientation of the spacecrafts.  They are an ultimate example for principle of angular momentum.  But here we are going to see the example using only flywheels because gyroscope is the combination of flywheels.

    

      

     Above picture describes a model of spacecraft with a flywheel mounted inside.  Let us imagine a spacecraft or a satellite or a telescope which is orientated in a particular direction.  Now to change the orientation to (say) left of the spacecraft, the mission controller at the ground operate the flywheel to rotate it to the right at some higher angular velocity.  As a result the spacecraft itself starts turn to the left.  When the spacecraft turned enough angle, the flywheel is stopped rotating, the spacecraft will also stop turning.

     How does the spacecraft turned without any use of thrusters?  This is because of Conservation of angular momentum.  Initially when it is oriented in a initial direction, the total angular momentum of the system is zero because there is no external force acting on it to produce torque (turning force).  Here the system is the combination of both spacecraft and flywheel.  When the flywheel is set to rotate in one direction, then the angular momentum of the system becomes (say) positive X value.  Even now as there is no external torque, the total angular momentum of the system should be as same as initial value(zero).  But here the total angular momentum became positive.  So, as to make the total angular momentum to be zero the spacecraft will rotate in opposite direction (say negative X value).  Thus the spacecraft turns.  Here as positive and negative X cancel each other, the total angular momentum will become zero as initial.  This will continue until the flywheel is stopped, the change in orientation of the spacecraft also stops. This is the actual simple physics behind the great achievements of human beings.

Note:  When the mission controller makes flywheel to rotate at high speed, the spacecraft will rotate in opposite direction only at very low speed. Huge variations of this rotational speeds are due to huge variations in rotational inertia of the flywheel and the spacecraft.  The flywheel has very low value of rotational inertia and the spacecraft has very large value of rotational inertia. (because the flywheel is so smaller than the spacecraft.)  In other words, if only when we rotate the flywheel of smaller rotational inertia at high speed (say 5000 radians per second), the spacecraft of higher rotational inertia only moves slowly (say 5 radians per second - one radians is equal to nearly 57 degrees).  (It will be more simple if you know about the Vector product rule)

      A real life example for this spacecraft orientation is, spacecraft Voyager 2, on its 1986 flyby of the planet Uranus (see the above GIF), was set into unwanted rotation by this flywheel effect.  Every time when its tape recorder was turned on at high speed.  As mentioned above, the spacecraft changed its orientation. So, the ground staff at the jet Propulsion laboratory(JPL) had to program the on-board computer to turn on counteracting thruster jet every time the tape recorder was turned on or off to move in a planned direction.  Interesting right!!!

This is how physics makes us understand great things simply.

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Althaf Ahmed

India