Physics GRE - Mechanics

Mechanics equations for physics GRE

Projectile motion x-equation

projectile motion y-equation

centripetal acceleration (uniform circular motion)

centripetal force (uniform circular motion)

translational kinetic energy

rotational kinetic energy

gravitational potential energy

spring potential energy

Potential energy change between two points (conservative force)

Gravitational force

Force, given potential

rolling without slipping

Work-Energy Theorem (including nonconservative forces)

Work-energy theorem, kinetic energy form

Work definition

Angular momentum definition

Angular momentum, extended body

Torque definition

Torque, in terms of angular momentum

centrifugal force

Coriolis force

moment of inertia, point particle

moment of inertia, extended body

parallel axis theorem

center of mass, extended body

center of mass, point particles

Lagrangian definition

Euler-Lagrange equation

momentum conjugate to q

Hamiltonian definition (general)

Hamiltonian definition (no explicit time or velocity dependence)

Hamilton’s equation for dp/dt

Hamilton’s equation for dq/dt

orbital Lagrangian (restricted form)

angular momentum, spherical coordinates

effective potential for orbits

reduced mass

Orbital total energy

Hooke’s law

spring angular frequency

spring solution (general form)

motion of springs in n-spring system

solving for normal frequencies in an n-spring system (secular equation)

oscillator with damping

resonant frequency of an oscillator

pendulum equation of motion, small displacements

pendulum angular frequency

angular frequency, extended object pendulum

Bernoulli’s Principle

fluid conservation equation