Topic 5.3 Torque: calculate the torque produced by a force as tau = rF sin(theta), and identify the lever arm and the sense of rotation.

What this topic is asking

The College Board (Topic 5.3) wants you to calculate the torque produced by a force about an axis, $\tau = rF\sin\theta$, to identify the lever arm (the perpendicular distance from the axis to the line of the force), and to determine the sense of the rotation (clockwise or counterclockwise). Torque is the rotational analogue of force: it is what causes angular acceleration.

What torque is

Torque answers the question "how effectively does this force cause rotation?" It depends not just on how hard you push, but on where and in what direction. The same force can produce a large torque or none at all, depending on the distance from the axis and the angle.

The lever arm and the angle

This is why a door handle is placed far from the hinges and you push perpendicular to the door: both maximize the torque. Pushing near the hinges, or pushing the door edge-on toward the hinge, produces little or no turning effect. The lever-arm idea, force times perpendicular distance, is often the quickest route to a torque.

The sense of rotation

A torque also has a direction of turning: clockwise or counterclockwise about the axis. In AP Physics 1 you assign one sense as positive (commonly counterclockwise) and the other as negative, then add torques with signs to find the net torque, exactly as you add forces with signs along an axis. The net torque determines whether and how the object's rotation changes. The physical reason torque, not force alone, governs rotation is that rotation is about turning around an axis, and a force's ability to turn something depends on its line of action relative to that axis. This is the rotational counterpart of how force governs translation: where $F_{net}$ drives linear acceleration through $F_{net} = ma$, the net torque $\tau_{net}$ drives angular acceleration through $\tau_{net} = I\alpha$ (Topic 5.6). Two forces of equal magnitude can produce wildly different torques, or even cancel, depending on their lever arms and senses. This is what makes torque the right quantity for rotational dynamics and equilibrium: a balanced object has zero net torque (Topic 5.5), and an object with a net torque undergoes angular acceleration. Computing torques correctly, attending to distance, angle and sense, is the gateway skill for the rest of the unit.

Try this

Q1. A $50$ N force is applied perpendicular to a wrench $0.30$ m from the bolt. Calculate the torque. [2 points]

• Cue. $\tau = rF\sin 90^\circ = (0.30)(50)(1) = 15$ N$\cdot$m.

Q2. A force is applied along the line from the axis to its point of application. Calculate the torque it produces. [1 point]

• Cue. $\theta = 0$, so $\tau = rF\sin 0^\circ = 0$. No torque.