Final answer:
Torque, also known as the moment of a force, is the product of the applied force and the lever arm, the perpendicular distance from the axis to the line of action of the force. Torque is critical for understanding rotational dynamics in physics.
Step-by-step explanation:
The magnitude of the moment of a force (or torque) about a fixed axis is calculated by multiplying the force by the perpendicular distance from the axis to the line of action of the force. This distance is known as the lever arm. The formula to calculate torque (moment) is represented as τ = r × F, where τ is the torque, r is the lever arm, and F is the force applied.
When a force is applied perpendicularly to the lever arm, the formula simplifies to τ = rF since the sine of 90 degrees (the angle between force and lever arm) is 1. If the angle is different from 90 degrees, then the formula includes the sine of the angle between the force and lever arm (τ = rF sin θ).
In the context of the examples provided, the calculation of torque is critical for understanding how forces cause objects to rotate around an axis, influencing both linear and angular motion according to the physical principles governing rotational dynamics.