Which expression below best describes the torque caused by...

Which expression below best describes the torque caused by force F3 = FE on B, the force that Earth exerts on the upper body at its center of mass for the backbone of length L? $$ \begin{array}{ll}{\text { (a) } 0} & {\text { (b) } F_{3}(2 L / 3) \sin 12^{\circ}} \\ {\text { (c) } F_{3}(L / 2) \cos 30^{\circ}} & {\text { (d) }-F_{3}(2 L / 3) \sin 12^{\circ}}\\ {\text { (e) }-F_{3}(L / 2) \cos 30^{\circ}}\end{array} $$

Which expression below best describes the torque caused by force F3 = FE on B, the force that Earth exerts on the upper body at its center of mass for the backbone of length L?
$$
\begin{array}{ll}{\text { (a) } 0} & {\text { (b) } F_{3}(2 L / 3) \sin 12^{\circ}} \\ {\text { (c) } F_{3}(L / 2) \cos 30^{\circ}} & {\text { (d) }-F_{3}(2 L / 3) \sin 12^{\circ}}\\ {\text { (e) }-F_{3}(L / 2) \cos 30^{\circ}}\end{array}
$$

Key Concepts

Torque

Torque is the measure of the rotational effect produced by a force applied at a distance from a pivot or axis. It is calculated as the product of the force magnitude and the lever arm, which is the perpendicular distance from the line of action of the force to the pivot point. This concept is fundamental in understanding how forces cause objects to rotate.

Lever Arm

The lever arm is the shortest distance between the axis of rotation (or pivot point) and the line along which the force acts. It is this perpendicular distance that multiplies the force to yield the torque, emphasizing the importance of both the magnitude of the force and its point of application relative to the pivot.

Center of Mass

The center of mass is the point at which the mass of an object is considered to be concentrated for the purposes of analysis, particularly when considering gravitational forces. In problems involving torque, the weight of an object acts through its center of mass, and its location relative to the pivot affects the magnitude and direction of the torque.

Force Decomposition

Force decomposition involves breaking a force vector into its components along chosen coordinate axes, typically using trigonometric functions such as sine and cosine. This process is crucial when determining the effective component of a force that contributes to torque in a particular direction, especially when the force is applied at an angle relative to the lever arm.

Sign Convention in Torque

Sign convention in torque pertains to the assignment of positive or negative signs to indicate the direction of the resulting rotational effect. A positive torque may be defined as causing counterclockwise rotation, while a negative torque causes clockwise rotation (or vice versa, depending on the chosen convention), thus providing clarity in the analysis of rotational dynamics.

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