Torque

 Torque, also known as turning force or moment, is a concept in physics and engineering that describes the tendency of a force to rotate an object about an axis. Understanding torque is essential in various fields, including mechanics, engineering, and physics. Here are some key points about torque:

1. Definition:

   • Torque ($�$) is defined as the product of force ($�$) and the perpendicular distance ($�$) from the axis of rotation to the line of action of the force.
   • Mathematically, torque is represented as $�=�\times �$.

2. Direction of Torque:

   • Torque is a vector quantity with both magnitude and direction.
   • The direction of torque is determined by the right-hand rule, which states that if you point your right thumb in the direction of the force and your fingers in the direction of the radius vector, then the torque is directed along your palm.

3. Units:

   • The SI unit of torque is the newton-meter (Nm).

4. rotational equilibrium:

   • An object is in rotational equilibrium when the net torque acting on it is zero. This is analogous to linear equilibrium, where the net force acting on an object is zero.

5. Moment Arm:

   • The perpendicular distance from the axis of rotation to the line of action of the force is often referred to as the moment arm. It plays a crucial role in determining the torque exerted by a force.

6. Calculation:

   • Torque can also be calculated using the angle ($�$) between the force vector and the lever arm: $�=�\times �\times \sin (�)$.

7. Applications:

   • Torque is fundamental in the operation of machines and engines, such as in the case of car engines, electric motors, and industrial machinery.
   • It is also important in understanding the mechanics of rotating objects and systems, like wheels, gears, and pulleys.

8. Torque and Angular Acceleration:

   • Torque is related to angular acceleration ($�$) through the equation $�=�\times �$, where $�$ is the moment of inertia of the object.

9. Conservation of Angular Momentum:

   • Torque is responsible for changes in angular momentum, and in the absence of external torques, the total angular momentum of a system is conserved.

Understanding torque is crucial in designing and analyzing mechanical systems, and it plays a significant role in solving problems related to rotational motion.