Torque is the rotational equivalent of force in linear motion: while force causes translational acceleration, torque causes angular acceleration of a rigid body around a fixed pivot. It is a core concept of Unit 6 Rotational Motion, which makes up 14-18% of the total AP Physics 1 exam score, appearing in both multiple-choice and free-response questions.
Unlike force, torque depends not just on the magnitude of the applied force, but also on where the force is applied relative to the pivot, and the direction of the force. A small force applied far from the pivot can produce the same torque as a large force applied very close to the pivot, the core principle behind levers and wrenches. Torque is denoted by the Greek letter $\tau$ (tau), and is sometimes called the *moment of force*.
2. Calculating Torque: Magnitude and Sign★★☆☆☆⏱ 4 min
There are two equivalent formulas for calculating torque that you will use on the AP Physics 1 exam. The standard definition formula is:
\tau = r F \sin\theta
where $r$ is the straight-line distance from the pivot to the point where the force is applied, $F$ is the magnitude of the applied force, and $\theta$ is the angle between the position vector $\vec{r}$ (from pivot to force) and the force vector $\vec{F}$.
An equivalent form using the lever arm (or moment arm) concept is:
\tau = F d_\perp
where $d_\perp = r \sin\theta$ is the perpendicular distance from the pivot to the line of action of the force. This form is often easier for visual problem-solving on the exam.
For fixed-axis rotation, the standard AP Physics 1 sign convention is: counterclockwise (CCW) rotation is caused by positive torque, and clockwise (CW) rotation is caused by negative torque. If a force's line of action passes directly through the pivot, $d_\perp = 0$, so torque is zero regardless of force magnitude.
Exam tip: If you get confused about which angle to use for $\theta$, always draw the full line of the force and measure the perpendicular distance from the pivot to that line—you can never go wrong with the lever arm method on the AP exam.
3. Torque from an Object's Weight★★☆☆☆⏱ 4 min
Any rigid body has weight distributed evenly across its mass, but the total torque from gravity around any pivot is equal to the torque produced by the entire weight of the object acting at its center of mass. This simplifies problem-solving significantly: you only need to locate the center of mass and treat weight as a single point force acting there.
For a uniform rigid body (constant density), the center of mass is always at the geometric center of the object. For example, a uniform beam of total length $L$ has its center of mass at $L/2$ from either end. Torque from weight is calculated the same way as any other torque:
\tau_g = r_{CM} mg \sin\theta
where $r_{CM}$ is distance from pivot to center of mass, $m$ is total mass of the object, and $g = 9.8 \, \text{m/s}^2$.
Exam tip: Never forget that the object's own weight produces torque unless the pivot is exactly at the center of mass. This is the most frequently omitted term in AP Physics 1 torque equilibrium problems.
4. Rotational Equilibrium★★★☆☆⏱ 5 min
Newton's first law extended to rotation states that if the net torque on a rigid body around a pivot is zero, the body has zero angular acceleration. This condition is called rotational equilibrium. If an object is also in translational equilibrium (net force on the object is zero), the entire system is in static equilibrium, meaning it is completely stationary—this is the most common type of torque problem tested on the AP exam.
\sum \tau = 0
This can also be written as $\sum \tau_{CCW} = \sum \tau_{CW}$, meaning total positive counterclockwise torques equal total negative clockwise torques. A key problem-solving trick for static equilibrium: you can choose any point as your pivot for calculating net torque, because net torque is zero around every point for a static system. Choosing the pivot at the location of an unknown force eliminates that force from the torque equation, letting you solve for other unknowns without force balance first.
Exam tip: Always choose your pivot at the location of an unknown force to eliminate that variable from your torque equation. This saves time and reduces algebra errors on FRQs.
5. Additional AP-Style Worked Examples★★★☆☆⏱ 5 min
Common Pitfalls
Why: Students mix up trigonometric terms from memorization instead of checking the formula definition
Why: Students focus on external applied forces and ignore the weight of the object itself
Why: Students do not set the convention at the start of the problem
Why: Students default to the only distance given in the problem, which is often the total object length
Why: Students forget that torque depends on distance from the pivot