Angular momentum and its applications

If you try to climb on a bicycle without a kickstand and then try to maintain balance, you will almost certainly fall off. However, as you begin pedalling, the angular momentum of these wheels increases. They are going to be resistant to change, which will make balance easier.

A rotating object’s angular momentum is defined as the attribute of any rotating object that is supplied by the product of the moment of inertia times the angle of rotation. It is a property of a rotating body that is defined as the product of the moment of inertia and the angular velocity of the spinning object (or object in motion). It is a vector quantity, which means that in addition to the magnitude, the direction is also taken into consideration here.

A skater’s angular acceleration when she moves her arms and legs close to the vertical axis of rotation is explained by the conservation of angular momentum, which may be seen in the figure below. By putting a portion of her body’s mass closer to the axis, she is able to reduce the moment of inertia of her body. In order for the angular momentum to remain constant (to be conserved), the angular velocity (rotational speed) of the skater must rise. This is because angular momentum is the combination of the moment of inertia and the angular velocity. When small stars (such as white dwarfs, neutron stars, and black holes) are generated from much larger and slower revolving stars, the same mechanism results in an extraordinarily quick spin of the compact stars (such white dwarfs, neutron stars, and black holes). When the size of an object is reduced by n times, the angular velocity of the object increases by a factor of n2 as a result of the reduction in size.

Conservation does not necessarily provide a complete explanation for the dynamics of a system, but it is a significant limitation on the system’s behaviour. Suppose a spinning top is subjected to gravitational torque, which causes it to lean over and change its angular momentum about the nutation axis. However, if friction at the point of spinning contact is ignored, the top has conserved angular momentum about its spinning axis and another about its precession axis. Aside from that, in every planetary system, the planets, star(s), comets, and asteroids can all move in a variety of sophisticated ways, but only so long as the total angular momentum of the system remains constant.

Law of conservation of angular momentum

It is the conserved quantity of angular momentum that we are currently researching. The letter L represents angular momentum in its simplest form. If no net external forces are present, much as linear momentum is conserved when there are no net external forces, angular momentum will be constant or conserved when there is no net external force.

It’s important to remember that things that are moving around a point have angular momentum. A significant physical quantity, because all experimental evidence shows that angular momentum in our Universe is rigidly conserved, meaning that it is only capable of being transferred rather than being either generated or destroyed. The amount of angular momentum assumes a straightforward shape in the simple situation of a small mass executing uniform circular motion around a much larger mass (such that we can ignore the effect of the centre of mass), as shown in the diagram. As shown in the adjacent figure, the magnitude of the angular momentum in this scenario is L = mvr, where L denotes the angular momentum, m denotes the mass of the little object, v denotes the magnitude of its velocity, and r denotes the distance between the two objects to be considered.

The implications of conservation of angular momentum 

An ice skater is spinning on the tip of her skate while her arms are out in front of her. Her angular momentum is conserved due to the fact that the net torque acting on her is negligible. When she draws in her arms, her rate of spin increases dramatically, resulting in a significant decrease in her moment of inertia in the next image. As a result of the effort, she expends to pull her arms closer together, she gains rotational kinetic energy.

 In order to retain its orientation, a gyroscope makes use of the notion of angular momentum. Three degrees of freedom are provided by a spinning wheel in this game. After being rotated at a high rate, it becomes locked onto the orientation and will not depart from that orientation until the rotation is stopped. This is particularly beneficial in space applications, where the attitude of a spacecraft is a critical factor that must be maintained under control.

There are numerous additional examples of objects that increase their rate of spin as a result of anything reducing their moment of inertia in their orbit. Tornadoes are an example of this. Storm systems that produce tornadoes rotate slowly as they approach. A tornado’s angular velocity increases when the radius of rotation narrows, even in a small geographic area, and can reach the level of a tornado’s fury in some cases. Another illustration is the planet Earth. It is believed that our planet was formed from a massive cloud of gas and dust, whose spin was caused by turbulence in an even larger cloud. In response to gravitational forces, the cloud contracted, and the rotation rate increased as a result of this. One would not anticipate that angular momentum would be retained when a body interacts with the environment, such as when a foot pushes off the ground, in the case of human motion. If astronauts are stationary while floating in space aboard the International Space Station, they have no angular momentum in relation to the interior of the spacecraft, which is the case. It makes no difference how much they twist and turn, as long as they do not push themselves off the edge of the vessel, their bodies will retain their zero value.

Conclusion

Angular momentum is the rotational analogue of linear momentum, and it is represented by the symbol l. In rotational motion, the cross product of two vectors is the product of their magnitudes multiplied by the sine of the angle formed by the body, and the cross product of two vectors in linear motion is the product of their magnitudes multiplied by the sine of the angle between them; the magnitude of a cross product of two vectors is always equal to the product of their magnitudes multiplied by the sine of the angle between them.