Torque, also known as the moment of force, is a measure of the rotational force applied to an object about a specific axis. It is a vector quantity, meaning it has both magnitude and direction. Torque is a crucial concept in mechanics and plays a fundamental role in understanding the motion and equilibrium of rotating objects.

Mathematically, torque ($\ufffd$) is calculated as:

$\ufffd=\ufffd\times \ufffd$

where:

- $\ufffd$ is the torque,
- $\ufffd$ is the distance from the axis of rotation to the point where the force is applied (also called the moment arm or lever arm),
- $\ufffd$ is the force applied perpendicular to the lever arm.

Units: The SI unit of torque is the newton-meter (N·m).

Key Points:

Rotational Effect:

- Torque is associated with the tendency of a force to rotate an object about an axis. It produces a rotational motion or changes the rate of rotation.

Direction:

- Torque is a vector quantity and has both magnitude and direction. The direction is determined by the right-hand rule, where the thumb points along the axis of rotation, and the fingers indicate the direction of the force.

Lever Arm:

- The lever arm (distance from the axis of rotation to the point where the force is applied) is a crucial factor in determining the torque. Increasing the lever arm or applying the force farther from the axis increases the torque.

Rotational Equilibrium:

- In a system in rotational equilibrium, the sum of the torques acting on the object is zero. This is known as the rotational analog of Newton's first law.

Applications:

- Torque is encountered in various everyday situations, such as opening a door, using a wrench, or turning a steering wheel. It is also a critical concept in mechanical engineering, robotics, and physics.

Example: Consider a wrench turning a bolt. The force applied to the wrench generates torque, and the longer the wrench (lever arm), the easier it is to turn the bolt. If the force is applied perpendicular to the wrench (lever arm), the torque is maximized.

In summary, torque is the rotational force that causes objects to rotate around an axis. It is an essential concept in mechanics and is applied in various engineering and physical contexts.

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