What is moment of force or torque? On what factors does it depend? Write its mathematical formula.

The moment of force (also called torque) is the rotational effect of a force about a point or axis. It is the product of the force applied and the perpendicular distance from the point of application of the force to the axis of rotation.

Factors that the moment of force depends on:

• Magnitude of the force (F): A greater force will produce a larger moment.
• Perpendicular distance (r): The distance from the point of rotation to the line of action of the force. The greater the distance, the larger the moment.
• Angle of application of the force: The force must be applied at an angle perpendicular to the lever arm (distance vector). If the force is not perpendicular, only the component of the force in the direction of the perpendicular distance contributes to the moment.

Mathematical formula:

τ=F×r

Where:

• $\tau$ is the torque (moment of force),
• $F$ is the force applied,
• $r$ is the perpendicular distance from the axis of rotation to the point where the force is applied.

In cases where the force is not perpendicular to the distance vector, the formula becomes:

τ=F×r×sin⁡(θ)

Where θ is the angle between the force and the line of action.