## Torque and Angular Momentum – Class 11 | Chapter – 7 | Physics Short Notes Series PDF for NEET & JEE

Torque and Angular Momentum: Torque and angular momentum are two important concepts in the study of rotational motion, and they are closely related to each other.

Torque is the measure of the force that causes an object to rotate around an axis. It is defined as the product of the force and the lever arm (perpendicular distance from the axis of rotation to the line of action of the force). The formula for torque is:

τ = r x F

Where,

• τ is the torque
• r is the lever arm
• F is the force applied perpendicular to the lever arm

Angular momentum is a measure of the amount of rotational motion of an object. It is defined as the product of the moment of inertia and the angular velocity of the object. The formula for angular momentum is:

L = Iω

Where,

• L is the angular momentum
• I is the moment of inertia
• ω is the angular velocity

## Relationship between Torque and Angular Momentum

Torque and angular momentum are closely related in the context of rotational motion. The relationship between these two quantities is described by the following equation:

τ = dL/dt

Where,

• τ is the torque
• L is the angular momentum
• d/dt is the derivative with respect to time

This equation states that torque is equal to the rate of change of angular momentum over time. In other words, if a torque is applied to a rotating object, its angular momentum will change over time. Similarly, if the angular momentum of a rotating object changes over time, it must be due to the presence of a torque.

The relationship between torque and angular momentum is particularly important in the design and optimization of rotating machinery, such as engines, turbines, and flywheels. By understanding the relationship between these two quantities, engineers can design systems that are efficient, stable, and safe. Overall, the relationship between torque and angular momentum is a fundamental concept in the study of rotational motion, with broad applications in physics, engineering, and other fields.

## Difference between Torque and Angular Momentum

 Torque Angular Momentum The calculation of the turning force of an object is known as torque Angular momentum is the calculation of the perpendicular distance from the force line of action to the rotation point Torque is represented as (τ) and it has the SI unit Nm/revolution Angular momentum symbol is denoted as M SI unit is NM Torque definition  is defined as a movement-related force Angular momentum is stated as a static force Coupling is measured by using torque. The angular momentum is not used for this type of purpose. Where there is the availability of rotation and torque is utilised The lateral force utilised in non-rotational events produces Angular Momentum Torque inclines a force to rotate on an object which is a pivot Angular movement is the concept that mentions the force used to move an object

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