Physics C: Mechanics · Unit 5: Rotation · 14 min read · Updated 2026-05-11
Torque and Rotational Statics — AP Physics C: Mechanics
AP Physics C: Mechanics · Unit 5: Rotation · 14 min read
1. Definition and Calculation of Torque★★☆☆☆⏱ 4 min
The general definition of torque comes from the cross product of the position vector $\vec{r}$ (from the pivot to the point of force application) and the applied force $\vec{F}$:
vec{tau} = vec{r} times vec{F}
The magnitude of torque is given by $\tau = rF\sin\theta$, where $\theta$ is the angle between $\vec{r}$ and $\vec{F}$ when placed tail to tail. An equivalent formulation using the lever arm (moment arm) $d = r\sin\theta$, the perpendicular distance from the pivot to the line of action of the force, simplifies static problems to $\tau = Fd$. The standard AP sign convention takes counterclockwise (CCW) torque as positive and clockwise (CW) torque as negative, matching the right-hand rule for cross products.
2. Equilibrium Conditions for Rotational Statics★★☆☆☆⏱ 3 min
For a rigid body to be completely static (no acceleration of any kind), two conditions must hold: translational equilibrium and rotational equilibrium. Translational equilibrium, from linear statics, means net force in all directions is zero:
sum vec{F} = 0 implies sum F_x = 0, quad sum F_y = 0
The new core condition for rotational statics is that net torque about any pivot point is zero:
sum tau = 0
A critical problem-solving simplification: if a system is in translational equilibrium, net torque is identical about any pivot point. You can choose any pivot to simplify calculations, and the most strategic choice is almost always a pivot at the location of an unknown force, since that force has $r=0$, so its torque is zero, eliminating the unknown immediately.
3. Complex Static Systems: Leaning Ladders★★★☆☆⏱ 4 min
Most AP C FRQ problems on rotational statics involve multi-force systems with multiple unknowns, requiring both force and torque equilibrium together to solve. The most common example is a uniform ladder leaning against a frictionless vertical wall, standing on a rough horizontal floor.
4. Practice Worked Examples★★★☆☆⏱ 3 min
Common Pitfalls
Why: Most problems give the angle between the force and the rod, so students confuse torque formulas with linear force component formulas.
Why: Students associate center of mass with all rigid body problems, so they default to it without strategic thinking.
Why: Students forget that weight is distributed evenly across the rigid body.
Why: Students focus on the new rotational condition and forget that static systems require both equilibria.
Why: Students don't write their sign convention explicitly, so they reverse directions when adding torques.