Torque and Angular Momentum

If the body is situated at a certain point, then its motion is known as rotational motion.

Rotational motion is also known as the change of state of a body to stipulate it with linear acceleration. Angular momentum and torque are the rotational equivalents of momentum and force. These two forces help change the rotational state of a natural object or a body. In our day-to-day life, we can see the functions of angular momentum and torque, which are very useful. 

Torque: Definition 

Torque definition can be defined as the force analogous in the instance of rotational motion. Let’s take an example of a door. The door position is initially fixed. It rotates only about its axis. Force is required to rotate the door, but the force is applied to the door on its hinge, but it does not work because force is not applied alone, but the position it is applied to also matters.

The equal force present in rotational motion is known as torque. It is also known as the moment of force, which causes the angular acceleration formula of the body, indicating the change of the rotational state of a body by force. 

Let a point P be a particle located very far from the origin at a certain point, having a position vector r unit vector. On the particle, if the force F is acting, the moment of force can be described as:

Torque formula = (F) x (r) where F and r are unit vectors.

The above equation is a vector quantity because it has a cross-product.

The magnitude of the torque formula can be defined as:

Torque = F.r.sin(θ)

Here, the “θ” is the angle present force and position vector,  and the “r” is the magnitude of the position vector. And “rsinθ” is the perpendicular distance of the force of the rigid body to the axis.

The concept of torque is derived from the studies of Archimedes on the utilisation of levers. Torque definition is described as the product of the perpendicular distance and magnitude of the force of the line of action of a force from the axis of rotation. 

Torque definition is known as pseudovector concerning three-dimension for a very minute or point particle.

Angular Momentum

Rotational motion is defined as the equal force applied to the torque. Linear momentum is analogous to the angular acceleration formula. Rotational Momentum is a conserved quantity, as the total angular momentum of the closed system remains the same or constant.

Angular momentum consists of both magnitude and direction and both are preserved or conserved. Angular momentum can be found in Frisbees, rifled bullets, motorcycles. All these have the conservation of angular momentum properties. 

Let P be the particle of linear momentum denoted “p” and O is the origin with respect to the position vector. The angular momentum can be described or denoted by “L.”

L = r × p.

The angular momentum magnitude can be described as:

L = rpsinθ,

Where p and r are the position vectors and linear momentum magnitude, respectively, the angle difference between linear momentum and position vector is denoted (θ).

Where “rsinθ” is the perpendicular angle between position vector and momentum.  

Torque and Angular Momentum: Difference

Conclusion

Angular momentum is the definition of physics and mathematics that indicates the propensity of a force that is used to move an object. On the other hand, torque is the inclination of a force used for object rotation in a pivot. Angular Momentum is defined as the perpendicular distance between the force of action’s line and the point of rotation, while torque is calculated as the turning force of an object. Torque is also used to calculate coupling and Angular Momentum is not used in these cases.