BlogNCERTImportant Topic of Physics: Angular Momentum

Important Topic of Physics: Angular Momentum

Introduction:

It is known that momentum is the product of mass and the velocity of the object. Any object or body moving with mass possesses momentum and the angular momentum is the property characterizing the rotary inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system. Even, the Earth has orbital angular momentum because of its annual revolution about the Sun and spin angular momentum because of its daily rotation about its axis. We can say that the magnitude of the angular momentum of an orbiting object is equal to its linear momentum (product of its mass m and linear velocity v) times of the perpendicular distance r from the center of rotation to the line drawn in the direction of its instantaneous motion and passing through the object’s center of gravity, or simply mvr.

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    The information about angular momentum from various physics-related articles are available here. Angular momentum and its concepts are important topics in physics. Students who want to flourish in physics need to be well known about momentum to get deep knowledge about it to do well on their exams. The examples, formula, and angular momentum quantum number are provided here to assist students in effectively understanding the respective topic. Continue to visit our website for additional physics help.

    Overview:

    The angular momentum of a rigid body can be considered as the product of the moment of inertia and the angular velocity and it is analogous to linear momentum. If there is no external torque on the object, then it is subject to the basic constraints of the conservation of angular momentum principle. The angular momentum and linear momentum are two examples of the parallels between linear and rotational motion. They both have the same form and are subject to the fundamental constraints of conservation laws, the conservation of momentum, and the conservation of angular momentum.

    Angular momentum is an important measure for studying dynamics on different temporal and spatial scales. We can conclude that the angular momentum in a closed system is constant in total but can be redistributed within that system and the transport of angular momentum is also done vertically, carrying angular momentum as part of the Hadley and other mean meridional circulations. So, the law of conservation of angular momentum then guarantees that the angular momentum of the particle is constant (again referred to as an origin at the center of the circle). The angular momentum is constant in magnitude and constant in direction (the motion is confined to a single plane, the plane of rotation).

    Angular Momentum:

    Angular momentum can be defined as the property of any rotating body given by moment of inertia times angular velocity.

    That is, it is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is clear that this is a vector quantity, along with magnitude, the direction is also considered.

    Symbol The angular momentum is a vector quantity, denoted by L
    Units It is measured using SI base units: Kg.m 2 s-1
    Dimensional formula The dimensional formula is: [M][L]2[ T]-1

    Angular Momentum Formula:
    Angular momentum can be experienced by a body in two situations.

    (1) Point object: It is the object accelerating around a fixed point.

    Consider the example:

    Earth revolves around the sun. Here the angular momentum is given by:

    L=r ×p

    Here,

    L= the angular velocity

    r = the radius (distance between the object and the fixed point about which it revolves)

    p = the linear momentum.

    (2) Extended object: It is the object, which is rotating about a fixed point.

    Consider the example:

    Earth rotates about its axis. Here the angular momentum is given by:

    L= I × ω

    Here,

    L= the angular momentum.

    I = rotational inertia.

    ω = the angular velocity.

    Angular Momentum Quantum Number:

    The angular momentum quantum number is synonymous with the Azimuthal quantum number or secondary quantum number. It can be said as a quantum number of an atomic orbital that decides the angular momentum and describes the size and shape of the orbital. Here, the value ranges from zero to one.

    Right-Hand Rule:

    It is used to give the direction of angular momentum

    It states that “If you position your right hand such that the fingers are in the direction of r. Then curl them around your palm such that they point towards the direction of Linear momentum(p). And, the outstretched thumb gives the direction of angular momentum(L).”

    Examples of Angular Momentum:

    (1) Ice skater:

    If an ice skater goes for a spin, then she starts off with her hands and legs far apart from the center of her body. But if she needs more angular velocity to spin, then she gets her hands and leg closer to her body. So, her angular momentum is conserved, and she spins faster.

    (2) Gyroscope:

    The gyroscope uses the principle of angular momentum to maintain its orientation. This uses a spinning wheel that has three degrees of freedom. If it is rotated at high speed it locks on to the orientation, it won’t deviate from its orientation. It is useful in space applications where the attitude of a spacecraft is a really important factor to be controlled.

    Also read: Conservation of Angular Momentum

    Frequently Asked Question (FAQs):

    Question 1: What is the expression for Angular momentum?

    Answer: The angular momentum can be expressed as,

    L= I × ω or L=r × p

    Question 2: How are angular velocity and radius related to an isolated rotating body?

    Answer: In the case of an isolated rotating body, the angular velocity is inversely proportional to the radius.

    Question 3: Write the dimensional formula for Angular momentum?

    Answer: The dimensional formula for angular momentum is M L 2 T-1.

    Question 4: What is an example of Angular momentum?

    Answer: If an ice skater goes for a spin, then she starts off with her hands and legs far apart from the center of her body. But if she needs more angular velocity to spin, then she gets her hands and leg closer to her body. So, her angular momentum is conserved, and she spins faster.

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