Free-body diagrams — AP Physics C: Mechanics
1. Core Definition and AP Exam Conventions ★★☆☆☆ ⏱ 3 min
A free-body diagram (abbreviated FBD) is a simplified vector diagram that isolates a single object or defined system of objects, showing only net external forces acting on the system, omitting internal forces and surrounding environment. FBDs are a foundational skill for all Newton's laws problems on the AP exam: while directly worth 2-4% of total points, they are required for nearly 30% of all exam points. On FRQs, incorrect FBDs cost points even if your final numerical answer is correct.
2. Force Classification and System Isolation ★★☆☆☆ ⏱ 4 min
The first step to drawing a correct FBD is defining your system boundary, then classifying all forces as external (originating from outside the system) or internal (originating from inside the system). Internal forces cancel per Newton's third law and are always omitted from the FBD. Next, separate forces into contact and non-contact categories:
- **Non-contact forces**: Act at a distance; only gravitational weight ($mg$) appears in AP Physics C: Mechanics, and it always acts straight down toward the center of the Earth.
- **Contact forces**: Require physical contact with another object; include normal force, tension, friction, drag, and applied pushes/pulls. Every contact point between the system and another object produces at least one contact force.
A reliable routine to avoid missed or extra forces is: 1) Draw weight first, 2) Trace the system outline and add one contact force for every point of contact with another object.
Exam tip: On AP FRQs, never draw net force or acceleration vectors on an FBD you are explicitly asked to draw. Only include individual actual forces acting on the system.
3. Internal vs External Forces for Connected Systems ★★★☆☆ ⏱ 3 min
When analyzing multiple connected objects (e.g., two blocks connected by a string over a pulley), you can draw a separate FBD for each object, or a single FBD for the entire combined system. The key rule is: internal forces (forces between objects inside the system boundary) cancel out and are omitted from the combined system FBD. Only external forces (from objects outside the system) are included.
Combined system FBDs save time when calculating the acceleration of the entire system, but if you need to find the force between two connected objects (e.g., tension in the connecting string), you must isolate the individual object to treat that internal force as an external force in its FBD.
Exam tip: If a problem asks for the force between two connected objects, never use only the combined system FBD to solve for it; always isolate the individual object.
4. Coordinate Alignment for Inclined Plane FBDs ★★★☆☆ ⏱ 4 min
Inclined planes are one of the most common FBD contexts on the AP exam. The standard convention to simplify calculations is to align the x-axis parallel to the incline surface, and the y-axis perpendicular to the incline. This means only the weight vector needs to be resolved into components, as all other forces (normal, tension, friction) already lie along one of the axes.
W_x = mg \sin\theta, \quad W_y = mg \cos\theta
where $ heta$ is the angle of the incline measured from the horizontal. A quick check to confirm you did not swap sine and cosine is to test the edge case: if $ heta = 0^\ heta$ (flat ground), $W_x = 0$ (no parallel component) and $W_y = mg$ (full weight perpendicular to the ground), which is correct. If $ heta = 90^\circ$ (vertical wall), $W_x = mg$ and $W_y = 0$, which is also correct.
Exam tip: If you forget which trig function matches which component, confirm with the $ heta = 0^\ heta$ edge case; this check takes 2 seconds and eliminates half of all common errors here.
5. AP-Style Concept Check ★★★☆☆ ⏱ 2 min
Common Pitfalls
Why: Students confuse momentum/kinetic energy with an actual force acting on the object, especially for moving objects no longer being pushed.
Why: Students default to flat-surface normal force direction instead of remembering normal force is always relative to the contact surface.
Why: Students mix up tension direction, drawing it toward the rope instead of away from the system.
Why: Students forget internal forces cancel, leading to an extra force in net force calculations that gives the wrong acceleration.
Why: Students confuse resolved components of weight with the original actual force vector.
Why: Students double-count gravitational force when combining multiple objects.