Conservation of Angular Momentum a simple explanation

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Imagine, you are sitting in a rotatable chair by holding dumbbells in your hands by keeping your hands on your lap.  Tell your friend to rotate you along with the chair with maximum force to attain fast rotation. Now your are rotating at high speed. Then stretch your hands by holding dumbbells like in the figure below.

 Now what you feel is, you rotate at high speed when you fold your hands and you rotate at low speed when you stretch the hands.  Seems simple right? 

How this happens?

Physics behind this is, Conservation of Angular Momentum.

Before seeing the definition, you have to know the above event in terms of Physics. (Which will be useful forever)

1.  The Force that your friend applied to rotate you is know as external torque.

Torque can be called as turning force.

We can say that when a force tends to rotate an object or acting on a rotating object then that force is called as torque. Its symbol is tau τ.

2.  Important: When you are rotating, mass of your body behaves differently (not as same as in rest position). For example, when you have a plate filled with some food and if you rotate holding the plate's center on a finger, the food goes to the edges and you will feel different mass now than earlier.  And this difference is due to difference in Rotational Inertia (I) of rotating system.  Rotational inertia is also known as Moment of Inertia (I).  Its symbol is I.

So, in your case of rotating chair, you will feel different mass while holding thumbles on your lap and different mass while stretching your hands along with the dumbbells.  It means that you have different rotational inertia in the above event of rotating chair. 

3.  When your friend applies a torque (turning force) on you and leave you, you will attain a final rotating speed.  Unless an another external torque acts on the system, you will rotate at same speed forever.  But in reality we have many hidden external forces like frictions which slowdown the rotational motion.  But if you neglect those frictions (just imagine ideal conditions) you will rotate at same speed called angular velocity.  Its symbol is omega ω.

Finally, we came near to the conclusion.

As we all know (hope you know 😜) Newton's second law that the total linear momentum of an isolated system remains constant. (p = mv). 

(Isolated means that the system is unattached or not in contact with any other external things)

So, Same as above mentioned law, for the rotating system, the total angular momentum of an isolated system remains constant. (L= Iω).

Simply we can say that the product of rotational inertia and the angular velocity is known as angular momentum. (L= I x ω)

Conservation of Angular Momentum:

When there is no external torque acts on the rotating system, the total angular momentum of the system remains constant.

According to your rotating chair case, you have two different situations of rotation in your isolated system (your friend is not holding you or you are not holding anything and neglect all frictions).  You rotate at higher angular velocity when you are holding dumbbells on your lap than stretched hands with dumbbells.  How this speed varies? This is actually due to conservation of angular momentum. Because, rotational inertia of your system is greater when you are stretching your hands than when you are holding dumbbells on your lap. We can say that when rotating speed increases the rotational inertia decreases and vise versa. Thus the Angular Momentum is conserved that means remains constant.

Another simple explanation to understand easily, when you stretch your hands along with dumbbells, the area of distribution of masses increases i.e., rotational inertia I increases.  Due to this increase in I we need more energy to rotate the system at the same speed.  But here as we considered an isolated system there is no external torque is acting to give that extra energy.  Thus we can say that, to compensate the increase in rotational inertia the angular velocity decrease and vice versa.  Therefore the Angular Momentum is conserved.

At the conclusion, using the knowledge of conversation of angular momentum we can understand familiar and unfamiliar phenomenon deeply.  Understand physics and enjoy the nature. For more clarification on more topics follow 

Althaf Ahmed

India

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