Mechanics

Velocity is the rate of change of displacement with respect to time.

Acceleration is the rate of change of velocity with respect to time.

Relates final velocity to initial velocity, acceleration, and time.

Relates position to initial conditions, acceleration, and time.

Relates velocity to position without explicit time dependence.

Displacement using average velocity.

Vertical motion under gravity, neglecting air resistance.

Horizontal range of a projectile launched from ground level.

Maximum height of a projectile.

Total time a projectile spends in the air.

Average velocity is the total displacement divided by total time elapsed.

The net force equals mass times acceleration. Newton's fundamental law.

Weight is the gravitational force on an object.

Friction opposes relative motion between surfaces.

Spring force is proportional to displacement, opposite in direction.

Resistive force on object moving through fluid.

Maximum velocity when drag equals weight.

The center of mass is the mass-weighted average position of a system.

Pressure is force per unit area, measuring how concentrated a force is.

Bulk modulus measures a material's resistance to uniform compression.

Work is energy transferred by a force over a displacement.

Energy possessed by an object due to its motion.

Energy stored due to position in gravitational field.

Elastic potential energy stored in a spring.

Power is the rate at which work is done.

Net work equals the change in kinetic energy.

Total mechanical energy is conserved in absence of non-conservative forces.

Momentum is mass times velocity, a conserved quantity.

Impulse equals change in momentum.

Final velocity after elastic collision where KE is conserved.

Objects stick together after collision. Maximum KE loss.

Ratio of relative speeds after and before collision. e=1 for elastic, e=0 for perfectly inelastic.

Rate of change of angular position.

Rate of change of angular velocity.

Relates linear and angular velocities.

Acceleration pointing toward center of circular path.

Net force required for circular motion.

Torque causes angular acceleration. τ = r × F.

Rotational equivalent of mass for a point mass.

Rotational analog of Newton's second law.

Kinetic energy due to rotational motion.

Rotational analog of linear momentum.

Rotational analog of v = v₀ + at. Relates angular velocity to time under constant angular acceleration.

Rotational analog of x = x₀ + v₀t + ½at². Relates angular position to time.

Rotational analog of v² = v₀² + 2a(x - x₀). Time-independent rotational kinematic equation.

Moment of inertia of a solid disk or cylinder rotating about its central axis.

Moment of inertia of a uniform solid sphere rotating about any diameter.

Moment of inertia of a thin uniform rod rotating about its center, perpendicular to its length.

Relates moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass.

Total kinetic energy of a rolling object is the sum of translational and rotational kinetic energies.

Newton's law of universal gravitation.

Gravitational field strength at distance r.

General gravitational potential energy (negative).

Velocity for circular orbit at radius r.

Kepler's third law for circular orbits.

Minimum velocity to escape gravitational field.

Gravitational acceleration at the surface of a spherical body.

Radius of an orbit with a specific period. For geosynchronous orbit, T equals the planet's rotation period.