Reference Library

Velocity is the rate of change of position; acceleration is the rate of change of velocity. Both are vectors.

With acceleration constant, integrating once gives velocity as a function of time and integrating again gives position.

With air resistance neglected, horizontal and vertical motion are independent: constant velocity horizontally, constant acceleration g downward vertically.

Velocities measured in different reference frames moving at constant velocity relative to one another add as vectors.

Newton's first law: an object retains constant velocity unless a net force acts on it — inertia. His second and third laws are stated below.

A free-body diagram isolates one object and shows every external force acting on it as a vector — weight, normal force, tension, applied force, friction — drawn separately from any force it exerts on something else. Summing components along chosen axes converts the diagram directly into Newton's second law.

Friction opposes relative sliding, or the tendency to slide, between two surfaces in contact.

An object moving on a circular path at any speed accelerates toward the centre, even if its speed is constant.

Work is the energy transferred to or from an object by a force acting through a displacement.

Kinetic energy is the energy of motion. Potential energy is stored energy that depends on position, released as work when that position changes.

In a system with only conservative forces doing work, the total mechanical energy stays constant.

Power is the rate at which energy is transferred or work is done.

Impulse is the effect of a force acting over time; it changes an object's momentum by exactly that amount.

In an isolated system — no net external force — total momentum does not change, however violently the parts of the system interact with each other.

In an elastic collision, kinetic energy is conserved along with momentum. In an inelastic collision it is not — kinetic energy is lost to heat, sound, or deformation. In a perfectly inelastic collision the objects stick together.

The centre of mass is the mass-weighted average position of a system; it moves as though all the system's mass were concentrated there and all external force applied there.

Angular position, velocity and acceleration describe rotation exactly as their linear counterparts describe straight-line motion.

Moment of inertia is the rotational counterpart of mass — a measure of how hard it is to change an object's rotation, dependent on how its mass is distributed relative to the axis.

Torque is the rotational counterpart of force: it measures the twisting effect of a force about a chosen axis.

Angular momentum is the rotational counterpart of momentum, and like momentum it is conserved whenever no net external torque acts.

An object is in static equilibrium when it has neither linear nor angular acceleration.

The centre of gravity is the point where the total weight of an object can be considered to act. In a uniform gravitational field it coincides exactly with the centre of mass.

Stress is force per unit area within a material; strain is the resulting fractional deformation.

An elastic modulus is the ratio of stress to strain for a given type of deformation, constant while the material remains within its elastic limit.

Every pair of point masses attracts one another with a force along the line joining them.

A mass sets up a gravitational field around it; another mass placed in that field acquires potential energy that depends on separation.

A satellite in a circular orbit is in free fall, with gravity supplying exactly the centripetal force needed.

Kepler's first law: planetary orbits are ellipses with the Sun at one focus. His second law: a line from the Sun to a planet sweeps out equal areas in equal times. The third law, below, follows directly from Newton's law of gravitation.

Pressure in a static fluid increases with depth, as each layer supports the weight of the fluid above it.

A fluid exerts a net upward force on any object submerged in it, because pressure is greater on the object's lower surface than on its upper surface.

For an incompressible fluid flowing through a pipe of varying cross-section, mass is conserved.

Along a streamline, the sum of pressure, kinetic energy density and gravitational potential energy density is constant — energy conservation applied to flowing fluid.