Short Answer:

Angular momentum is the quantity of rotational motion possessed by a rotating body. It depends on the mass, shape, and rotational speed of the body. It is defined as the product of the moment of inertia and the angular velocity of the body. Angular momentum represents how difficult it is to change the rotational motion of an object.

In simple terms, just like linear momentum describes straight-line motion, angular momentum describes circular or rotational motion. It is a vector quantity, meaning it has both magnitude and direction, and it remains constant if no external torque acts on the body.

Detailed Explanation:

Angular Momentum

Angular momentum is one of the most important quantities in the study of rotational motion. It measures the amount of rotation a body has and how resistant it is to changes in its spinning motion. Every object that is rotating around an axis possesses angular momentum.

Mathematically, angular momentum is given by:

where,
= angular momentum,
= moment of inertia of the body about the axis of rotation,
= angular velocity of the rotating body.

This equation shows that angular momentum depends on how mass is distributed about the axis (through moment of inertia) and how fast the body is spinning (through angular velocity). The greater the moment of inertia or angular velocity, the greater will be the angular momentum of the body.

Concept of Angular Momentum

Angular momentum can be compared to linear momentum in translational motion. In linear motion, momentum  , where   is mass and   is velocity. Similarly, in rotational motion, angular momentum  , where   plays the same role as mass and   plays the same role as velocity.

Thus, angular momentum is a rotational equivalent of linear momentum. It shows the tendency of a rotating body to continue spinning unless acted upon by an external torque.

Direction of Angular Momentum

Since angular momentum is a vector quantity, it has both magnitude and direction. The direction of angular momentum is along the axis of rotation and is determined by the right-hand rule. According to this rule:
If you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of angular momentum.

For example, if a wheel rotates in a clockwise direction when viewed from the top, the angular momentum vector points downward, along the axis of rotation.

Conservation of Angular Momentum

One of the most important principles associated with angular momentum is its conservation. The law of conservation of angular momentum states that:
“If no external torque acts on a system, the total angular momentum of the system remains constant.”

This means that if a body is rotating and no external force or torque is applied to it, it will continue to rotate with the same angular momentum.

Mathematically,

or

This principle explains many natural and mechanical phenomena.

For example:

• A figure skater spins faster by pulling her arms closer to her body because reducing the moment of inertia increases the angular velocity to keep angular momentum constant.
• Planets maintain their rotational motion around the Sun because there is no external torque acting on them.

Factors Affecting Angular Momentum

1. Moment of Inertia (I):
   The moment of inertia depends on how the mass of the body is distributed around the axis of rotation. If the mass is far from the axis, the moment of inertia is large, leading to higher angular momentum for the same angular speed.
2. Angular Velocity (ω):
   The rate at which the body rotates also affects angular momentum. Higher angular velocity means greater angular momentum.
3. Mass Distribution:
   If the shape or structure of a rotating object changes, its moment of inertia changes, and to conserve angular momentum, its angular velocity changes accordingly.
4. External Torque:
   The presence of an external torque can change the direction or magnitude of angular momentum. The rate of change of angular momentum equals the applied torque:

where   is torque and   is angular momentum.

Practical Examples of Angular Momentum

1. Rotating Wheel:
   When a rotating wheel is set in motion, it tends to continue spinning due to its angular momentum unless a braking force (torque) is applied.
2. Spinning Top:
   A spinning top remains upright while spinning due to the conservation of angular momentum. When it slows down, the angular momentum decreases, and the top starts to fall.
3. Earth’s Rotation:
   The Earth spins around its axis with constant angular momentum. Changes in this momentum can cause variations in day length over geological time scales.
4. Figure Skater or Diver:
   When a figure skater pulls in their arms, they spin faster. Similarly, a diver can control their spinning speed during a somersault by changing body position — all due to conservation of angular momentum.

Conclusion

Angular momentum is a fundamental concept that describes the rotational motion of a body. It is the product of moment of inertia and angular velocity and determines how difficult it is to change the rotational state of an object. The direction of angular momentum is given by the right-hand rule, and its total value remains constant if no external torque acts on the system. Understanding angular momentum is essential in engineering, astronomy, and mechanical systems involving rotation, as it explains stability, spinning, and motion control.