What is Conservation of angular momentum?

However, if the system does not have a net external couple, you assume ∑τ⃗ = 0. In this case, the law of conservation of angular momentum can be introduced.

To learn how conservation law of angular momentum works, you can take the help of angular training in Hyderabad. This angular online training will help you in understanding the conservation law by the medium of demonstrations. This training also assures you angular certification after the successful completion of the training.

The conservation law of angular momentum

The angular online training will tell you how angular momentum of the particle system around a point in the fixed inertia reference frame is stored in the absence of a net external couple around that point.

dL ⃗ dt = 0 (11.4.1)

Or

L⃗ = l⃗1 + l⃗2 + ⋯ + l⃗N = constant. (11.4.2)

Note that the total angular momentum L is preserved. Individual angular moments can change as long as their sum is constant. This law is similar to the momentum that is conserved when the system's external forces are zero.

Due to the relatively low friction between the skates and the ice, the net torque is very close to zero. Also, friction occurs very close to the pivot point. As a result, it can rotate for quite some time. You can also increase the rotation speed by pulling the arms and legs inward. Why does pulling on my arms and legs increase the speed of rotation? The answer is that its angular momentum is constant.

L'= L (11.4.3)

Or

I'ω'= Iω, (11.4.4)

Here, the prepared amount refers to the condition after she has been pulled by his arm and reduced the moment of her inertia. Since I'is small, it is necessary to increase the angular velocity ω'to keep the angular momentum constant.

The ice skater spins on the toes of the skate with his arms outstretched. Its net torque is negligibly small, so its angular momentum is preserved. (B) If you pull the arm, the rotation speed will increase significantly, and the moment of inertia will decrease. The work of pulling the arm increases the rotational kinetic energy.

It is interesting to see how the skater's rotational kinetic energy changes as the skater pull his arm inward. Its initial rotational energy is

KRot = 12Iω2, (11.4.5)

Its final rotational energy

K'Rot = 12I (ω') 2. (11.4.6)

Since I'ω'= Iω, you can find it by inserting ω'.

K'Rot = 12I'(ω') 2 = 12I'(II'ω) 2 = 12I ω2 (II') = KRot (II'). (11.4.7)

As its moment of inertia decreased, I'<I, its final rotational kinetic energy increased. The source of this additional rotational kinetic energy is the work required to pull the arm inward. Note that the skater's arm spirals inward rather than in a perfect circle. This work increases the rotational kinetic energy, but its angular momentum remains constant. In a friction-free environment, no energy leaks from the system. Therefore, when the arm is extended to its original position, it rotates at the original angular velocity and the kinetic energy returns to the original value.

The solar system is another example of how conservation of angular momentum. If you do angular training in Hyderabad, we will show you how conservation of angular momentum works in our universe. The solar system was born out of a huge cloud of gas and dust that initially had rotational energy. Gravity caused the clouds to contract, preserving angular momentum and increasing rotational speed.

Initially, the gas cloud is rotating at an omega angular velocity and has an angular momentum L. It forms a fairly continuous disk on the surface of revolution. The disc then spins at an omega prime angular velocity but still has an angular momentum L. The disc begins to break into concentric rings—the space between the rings increases. Finally, the gas in the ring forms a star in the centre, and the orbit of the planet traces the ring from which they originate. In all cases, the angular velocity is in the same direction as the original gas cloud, and the angular momentum is L.

A solar system that combines originally spinning clouds of gas and dust. The orbital motion and spin of the planet are in the same direction as the original spin and retain the angular momentum of the parent cloud.

As the rotational inertia of the system increased, the angular velocity decreased, as expected from the law of conservation of angular momentum. In this example, you can see that the final kinetic energy of the system is reduced because the flywheel coupling loses energy.

In the end, you can learn how the conservation of angular momentum works in practical life by doing an angular certification Training.