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

Which expression below best describes the torque caused by force $F_{2}=T_{\text { M on } \mathrm{B}}$ exerted by the muscle on the backbone? $\begin{array}{ll}{\text { (a) } 0} & {\text { (b) } F_{2}(2 L / 3) \sin 12^{\circ}} \\ {\text { (c) } F_{2}(L) \cos 30^{\circ}} & {\text { (d) }-F_{2}(2 L / 3) \sin 12^{\circ}}\\ {\text { (e) }-F_{2}(L) \cos 30^{\circ}}\end{array}$ $$ $$

Which expression below best describes the torque caused by force $F_{2}=T_{\text { M on } \mathrm{B}}$ exerted by the muscle on the backbone?
$\begin{array}{ll}{\text { (a) } 0} & {\text { (b) } F_{2}(2 L / 3) \sin 12^{\circ}} \\ {\text { (c) } F_{2}(L) \cos 30^{\circ}} & {\text { (d) }-F_{2}(2 L / 3) \sin 12^{\circ}}\\ {\text { (e) }-F_{2}(L) \cos 30^{\circ}}\end{array}$

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Key Concepts

Torque

Torque is a measure of the rotational effect of a force acting about a pivot point. It is defined mathematically as the product of the force magnitude and the perpendicular (or effective) distance (known as the moment arm) from the pivot to the line of action of the force. This rotational influence depends not only on the size of the force but also on where and how it is applied.

Moment Arm

The moment arm is the effective lever length at which a force acts to produce rotation. It is the perpendicular distance from the pivot point to the force's line of action. Often, this is calculated using trigonometric functions (like sine or cosine) that relate the actual distance from the pivot to the angle between the force direction and the line from the pivot.

Sign Convention in Torque

The sign of the torque indicates the direction of the rotation produced by the force. A positive value might be defined for counterclockwise rotation and a negative value for clockwise rotation (or vice versa, depending on the convention used). Understanding and correctly applying this sign is crucial when summing torques, as it determines the net rotational effect around the pivot.

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