Physics C: Mechanics Study Library.

Scalars and vectors; displacement, velocity, acceleration · Representing motion: position-time, velocity-time, and acceleration-time graphs · Reference frames and relative motion · Motion in two or three dimensions: projectile motion, circular motion · Derivatives of position functions: v(t) = dx/dt, a(t) = dv/dt · Integration for displacement: x = x₀ + ∫v dt · Non-constant acceleration problems requiring calculus methods

Systems and center of mass · Forces and free-body diagrams · Newton's First, Second, and Third Laws · Gravitational force; kinetic and static friction · Spring forces (Hooke's Law) · Resistive forces: drag proportional to v and to v² · Setting up and solving differential equations for resistive-force motion (separation of variables) · Circular motion: centripetal acceleration and net centripetal force

Translational kinetic energy · Work done by variable forces: W = ∫F·dx · Work-energy theorem · Conservative vs. non-conservative forces · Potential energy functions derived from force: U = -∫F dx · Conservation of mechanical energy · Energy dissipation by non-conservative forces · Power: P = dW/dt = F·v

Linear momentum (p = mv) · Impulse and the impulse-momentum theorem: J = ∫F dt = Δp · Conservation of linear momentum · Elastic collisions (kinetic energy conserved) · Inelastic and perfectly inelastic collisions · Two-dimensional collision analysis · Center of mass position and velocity for discrete and continuous mass distributions · Center of mass integrals for uniform objects

Rotational kinematics: angular displacement, angular velocity, angular acceleration · Kinematic relationships between linear and rotational quantities: v = rω, a_t = rα · Torque: τ = r × F (magnitude τ = rF sinθ) · Rotational inertia (moment of inertia): I = ∫r² dm · Parallel-axis theorem: I = I_cm + Md² · Rotational equilibrium: Στ = 0 · Newton's Second Law for rotation: τ_net = Iα · Connecting translational and rotational Newton's Second Law for systems with both

Rotational kinetic energy: K_rot = ½Iω² · Work done by a torque: W = ∫τ dθ · Angular momentum of a rigid body: L = Iω · Angular impulse: J_ang = ∫τ dt = ΔL · Conservation of angular momentum (conditions: zero net external torque) · Rolling without slipping: constraint v_cm = rω; total KE = ½mv² + ½Iω² · Combined energy conservation for rolling objects on inclines · Orbital mechanics and satellite motion (gravitational potential energy, circular orbits)

Defining Simple Harmonic Motion (SHM): restoring force proportional to displacement · The SHM differential equation: d²x/dt² = −ω²x · General solution: x(t) = A cos(ωt + φ) · Period and frequency for a mass-spring system: T = 2π√(m/k) · Period and frequency for a simple pendulum: T = 2π√(L/g) (small-angle approximation) · Velocity and acceleration as functions of time in SHM · Energy of SHM: total mechanical energy E = ½kA² = ½mv²_max; KE-PE exchange · Physical pendulums: T = 2π√(I/mgd); requires moment of inertia