Show that the magnitude of torque = magnitude of force x moment arm. Also show that only the angular component of the force is responsible for producing torque.

The magnitude of torque is defined as the product of the magnitude of the force applied and the moment arm, which is the perpendicular distance from the axis of rotation to the line of action of the force. This relationship highlights that the effectiveness of a force in generating rotation depends on both the size of the applied force and its distance from the axis. If the force is applied directly at the pivot, then the moment arm is zero, and torque is not produced. However, in the case of application of force with an angle to the pivot, the moment arm can be a maximum, giving a greater torque effect.

Furthermore, only the angular component of the force results in the torque. This is because torque is produced by the force that acts perpendicular to the radius vector, which results in rotation. If a force is applied at an angle to the radius vector, only the component perpendicular contributes to the torque. The component of the force that acts parallel to the radius does not produce rotational motion because it merely pulls or pushes toward the axis without causing rotation. Therefore, understanding the magnitude of the force and the angle at which it is applied is critical in analyzing rotational motion.

See more : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/