AP Physics C: Mechanics · Unit 2 · Topic 2.10

Circular Motion

Vector force models and differential equations determine center-of-mass motion in constrained and curving systems.

Force-time interaction · Circular MotionThe signed area under the force-time graph equals impulse and therefore the change in momentum.

1. Topic Lens

Circular Motion is studied through force and translational dynamics. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[\sum\vec F=\frac{d\vec p}{dt}\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

For constant mass, momentum p=mv gives dp/dt=m dv/dt.
When force is position-dependent, apply the chain rule dv/dt=(dv/dx)(dx/dt).
Since dx/dt=v, the equation becomes F=mv dv/dx and can be integrated.

\[\sum F_x=m\frac{dv}{dt}=mv\frac{dv}{dx}\]

3. Detailed Visual Model

**Circular Motion**Topic-matched fine pixel-art model · use the lesson's equations and labeled diagrams for exact scientific meaning.

4. Worked Example and Lab Link

A constant net force of 8 N acts on a 2 kg mass. Find acceleration.

Answer: a=8/2=4 m/s².

Investigation idea: Measure force and acceleration for a changing-mass cart system and compare a numerical differential-equation model.

Common trap: Centripetal force is the inward net force, not an extra force to add to the free-body diagram.

Checkpoint · Topic 2.10

Explain how circular motion supports or limits this conclusion: a=8/2=4 m/s².

Official curriculum reference: College Board AP Physics C: Mechanics course page. The explanation and worked example are independently written for this study site.