Inside This Unit: The Full Breakdown
This unit applies Newton’s laws with free-body diagrams to translational motion, including friction, tension, inclines, and velocity-dependent resistive forces that require solving differential equations.
Why it matters
Dynamics is the heart of mechanics. The differential-equation treatment of drag and terminal velocity is a distinctly Physics C skill.
Key concepts
- ΣF = ma = m(dv/dt) is applied per object using free-body diagrams.
- Static friction is variable (≤ μ_s N); kinetic friction is μ_k N.
- On an incline, weight components are mg sinθ and mg cosθ.
- Resistive forces (F = −bv) give m dv/dt = mg − bv and a terminal velocity where net force is zero.
Newton’s Laws and Free-Body Diagrams
Begin every problem with a free-body diagram, then write ΣF = ma along chosen axes. Action-reaction pairs act on different objects. On inclines, resolve gravity into components; the normal force is mg cosθ, less than the full weight.
Resistive Forces and Terminal Velocity
When a force depends on velocity (drag F = −bv), Newton’s second law becomes a differential equation m dv/dt = mg − bv. Solving it shows velocity approaching terminal velocity, where the resistive force balances gravity and acceleration is zero.
AP exam tip
For drag problems, set net force to zero to get terminal velocity quickly, and recognize the exponential approach when asked for v(t).
Connections to other units
- Unit 1: Forces produce the accelerations analyzed kinematically.
- Unit 3: The work done by these forces changes energy.
