Sign in to save

Bookmark this page so you can find it later.

Sign in to save

Bookmark this page so you can find it later.

AP Physics C Mechanics Formula Sheet cheat sheet - grade 11-12

Click image to open full size

Physics Grade 11-12

AP Physics C Mechanics Formula Sheet Cheat Sheet

A printable reference covering kinematics, Newton's laws, work-energy, momentum, rotation, gravitation, and simple harmonic motion for grades 11-12.

TopicsMotionNewton's LawsEnergyMomentumRotationGravityStudy GuideAP Physics
Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

Study as Flashcards

AP Physics C Mechanics uses calculus to describe motion, forces, energy, momentum, rotation, gravitation, and oscillations. This cheat sheet helps students organize the main equations and decide which model fits a problem. It is especially useful for reviewing before quizzes, unit tests, and the AP exam.

The formulas connect derivatives, integrals, vectors, and physical meaning.

Key Facts

  • Linear kinematics connects position, velocity, and acceleration by v=dxdtv = \frac{dx}{dt}, a=dvdta = \frac{dv}{dt}, and Δx=∫t1t2v dt\Delta x = \int_{t_1}^{t_2} v\,dt.
  • Newton's second law is ∑F⃗=ma⃗\sum \vec{F} = m\vec{a} for constant mass, and equilibrium requires ∑F⃗=0⃗\sum \vec{F} = \vec{0}.
  • Work and energy are connected by W=∫F⃗⋅dr⃗W = \int \vec{F}\cdot d\vec{r} and Wnet=ΔKW_{\text{net}} = \Delta K, where K=12mv2K = \frac{1}{2}mv^2.
  • Linear momentum is p⃗=mv⃗\vec{p} = m\vec{v}, impulse is J⃗=∫F⃗ dt=Δp⃗\vec{J} = \int \vec{F}\,dt = \Delta \vec{p}, and total momentum is conserved when external impulse is zero.
  • Rotational motion uses ω=dθdt\omega = \frac{d\theta}{dt}, α=dωdt\alpha = \frac{d\omega}{dt}, τ=Iα\tau = I\alpha, and Krot=12Iω2K_{\text{rot}} = \frac{1}{2}I\omega^2.
  • Angular momentum is L⃗=Iω⃗\vec{L} = I\vec{\omega} for rotation about a fixed axis, and L⃗\vec{L} is conserved when the net external torque is zero.
  • Newtonian gravitation uses Fg=Gm1m2r2F_g = \frac{Gm_1m_2}{r^2}, Ug=−GMmrU_g = -\frac{GMm}{r}, and circular orbit speed v=GMrv = \sqrt{\frac{GM}{r}}.
  • Simple harmonic motion satisfies a=−ω2xa = -\omega^2x, with spring angular frequency ω=km\omega = \sqrt{\frac{k}{m}} and period T=2πmkT = 2\pi\sqrt{\frac{m}{k}}.

Vocabulary

Derivative
A derivative gives an instantaneous rate of change, such as v=dxdtv = \frac{dx}{dt} for velocity.
Integral
An integral accumulates a changing quantity, such as W=∫F⃗⋅dr⃗W = \int \vec{F}\cdot d\vec{r} for work.
Net Force
Net force is the vector sum of all forces acting on an object, written as ∑F⃗\sum \vec{F}.
Torque
Torque measures the rotational effect of a force and is given by τ⃗=r⃗×F⃗\vec{\tau} = \vec{r}\times \vec{F}.
Moment of Inertia
Moment of inertia II measures how mass is distributed relative to an axis of rotation.
Conservative Force
A conservative force has path-independent work and can be described by potential energy with F⃗=−∇U\vec{F} = -\nabla U.

Common Mistakes to Avoid

  • Using constant-acceleration equations when acceleration is not constant is wrong because equations like v2=v02+2aΔxv^2 = v_0^2 + 2a\Delta x require constant aa.
  • Dropping vector signs in force and momentum problems is wrong because directions determine signs and components in ∑F⃗=ma⃗\sum \vec{F} = m\vec{a} and ∑p⃗i=∑p⃗f\sum \vec{p}_{i} = \sum \vec{p}_{f}.
  • Confusing work with force is wrong because work depends on displacement and angle through W=∫F⃗⋅dr⃗W = \int \vec{F}\cdot d\vec{r}.
  • Using τ=rF\tau = rF for every torque problem is wrong because the correct magnitude is τ=rFsin⁡θ\tau = rF\sin\theta or the force times the lever arm.
  • Treating angular momentum as always L=IωL = I\omega is wrong because for a particle the general form is L⃗=r⃗×p⃗\vec{L} = \vec{r}\times \vec{p}.

Practice Questions

  1. 1 A particle moves along the xx-axis with v(t)=3t2−4tv(t) = 3t^2 - 4t in meters per second. Find its displacement from t=0t = 0 to t=2 st = 2\,\text{s}.
  2. 2 A 2.0 kg2.0\,\text{kg} block is pulled by a variable force F(x)=5xF(x) = 5x in newtons from x=0x = 0 to x=3.0 mx = 3.0\,\text{m}. Find the work done.
  3. 3 A solid disk with I=12MR2I = \frac{1}{2}MR^2 has M=4.0 kgM = 4.0\,\text{kg}, R=0.30 mR = 0.30\,\text{m}, and ω=12 rad/s\omega = 12\,\text{rad/s}. Find its rotational kinetic energy.
  4. 4 A comet speeds up as it falls toward the Sun. Explain why angular momentum can remain constant while kinetic energy changes.

Understanding AP Physics C Mechanics Formula Sheet

A formula sheet becomes useful only after you identify the system and the time interval being studied. The system might be one block, two colliding carts, a rolling wheel, or a satellite. Draw it first.

A free body diagram shows forces acting on the chosen object, not forces it exerts on something else. Choose axes that simplify the motion. On an incline, axes parallel and perpendicular to the surface usually reduce the work.

Resolve every angled force into components before adding forces. Keep signs consistent. A negative answer often carries physical information, such as motion opposite to the positive direction or a force that opposes the assumed direction.

Calculus helps when motion or force changes continuously. A slope tells you a rate at one instant. The slope of a position versus time graph gives velocity.

The slope of a velocity versus time graph gives acceleration. Area has a different meaning. The area under a velocity versus time graph gives displacement, while the area under a force versus time graph gives the accumulated effect of a force.

Students should always check the graph labels before interpreting area. A curved graph does not automatically mean acceleration is increasing. Its changing slope must be examined.

Units provide a quick error check. An answer for energy must have energy units, not force units or speed units.

Conservation methods are often shorter than tracking every moment of motion, but their conditions matter. Energy methods work well when you can account for each transfer. Friction changes organized mechanical energy into thermal energy.

It does not make energy disappear. Momentum methods are especially useful during impacts because collision forces can be large but act for a short time. Internal forces between objects in a chosen system cancel in pairs when considering total momentum.

External forces do not cancel. A floor can provide an important external impulse during a collision.

Decide whether the event is isolated enough before claiming a conserved quantity. State the time interval clearly, since a quantity may be conserved during the brief collision but not throughout the full trip.

Rotation follows many of the same ideas as straight line motion, yet the distance from the axis changes everything. A force applied farther from a hinge can produce a larger turning effect. This explains why door handles are placed far from their hinges.

Mass far from an axis makes an object harder to speed up rotationally. For rolling objects, track both the motion of the center of mass and the spinning motion. Rolling without slipping links them, but sliding does not.

In gravitation, distance is measured from center to center, which matters for planets and satellites. In oscillations, the restoring effect points toward equilibrium. At the turning points, speed is zero and stored energy is greatest.

At equilibrium, speed is greatest. These patterns help students predict an answer before calculating it.