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

Which expression below best describes the torque caused by force F4 = FDonB, the force that the disk in the lower back exerts on the backbone of length L? $$ \begin{array}{l}{\text { (a) } 0 \qquad \text { (b) } F_{4}(2 L / 3) \sin 12^{\circ}} \\ {\text { (c) } F_{4}(L) \cos 30^{\circ}} \\ {\text { (e) }-F_{4}(L) \cos 30^{\circ}}\end{array} $$

Which expression below best describes the torque caused by force F4 = FDonB, the force that the disk in the lower back exerts on the backbone of length L?
$$
\begin{array}{l}{\text { (a) } 0 \qquad \text { (b) } F_{4}(2 L / 3) \sin 12^{\circ}} \\ {\text { (c) } F_{4}(L) \cos 30^{\circ}} \\ {\text { (e) }-F_{4}(L) \cos 30^{\circ}}\end{array}
$$

Key Concepts

Torque

Torque is a measure of the tendency of a force to rotate an object about an axis. It is defined mathematically as the cross product of the position (lever arm) vector and the force vector, meaning it depends on both the magnitude of the force and its distance from the pivot point as well as the angle between the force and the lever arm.

Lever Arm

The lever arm is the distance from the axis of rotation to the point where the force is applied. In torque calculations, it is crucial because a longer lever arm increases the capability of a force to produce rotation.

Moment Arm

The moment arm is the perpendicular distance from the axis of rotation to the line along which the force acts. This concept refines the idea of the lever arm by focusing on the effective distance that actually contributes to rotational motion.

Trigonometric Components in Torque

Trigonometry plays a key role in torque calculations, where the angle between the force direction and the lever arm must be considered. Typically, the sine function is used because it gives the component of the force that is perpendicular to the lever arm, which is the effective part in generating rotation.

Sign Convention in Torque

In analyzing torque, specifying a sign convention is important. Positive and negative values generally denote the direction of rotation (for example, counterclockwise being positive and clockwise being negative), aiding in the proper summing and balancing of torques in a system.

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