Module 5: Advanced Mechanics

Law of Universal Gravitation

F = Gm₁m₂ / d²

range

the horizontal displacement of an object from its launching point

trajectory

the path of a projectile

terminal velocity

constant velocity attained for a falling object

• drag force is equal and opposite to weight force → F_net = 0

air resistance (drag)

air particles that apply a friction force on the projectile

projectile

an object that is projected into the air, but not propelled as in a rocket

centripetal force

the force that keeps an object moving in a circle, pointing straight toward the center of the path

circular motion (in a magnetic field)

created when a net force supplied by the interaction of the charged particle with the magnetic field IS the centripetal force

tension

a pulling force acting through a medium such as a rope or chain

banked (curve)

making the corner angled with respect to the ground

angular velocity (curly w)

measured in radians/second

stroboscopic image

a photograph that captures multiple sequential phases of a moving subject within a single frame (e.g. at 100Hz frequency)

kinetic energy

the energy associated with motion

potential energy

energy associated with it due to its position relative to another object or within a field

mechanical energy (E_m)

the sum of potential and kinetic energy

Principle of Conservation of Mechanical Energy

If in a system of bodies, there are no other forms of energy except kinetic and potential energy, then the total mechanical energy of the system is constant, ie. (E_m)_initial = (E_m)_final

torque

rotational effect that a force has on an object

satellite

any object that is orbiting the Earth, Sun or other massive body

orbital radius

= radius of central body + altitude of satellite

Kepler’s First Law (the law of ellipses)

Each planet moves, not in a circle, but in an ellipse, with the sun, off centre, at focus.

Kepler’s Second Law (the law of equal areas)

As the planet travels around the orbit, the area covered by a line joining the sun to the planet sweeps out equal area in equal times

Kelper’s Third Law (the law of periods)

For all planets, the cube of the average radius is proportional to the square of the orbital period; that is, r³/T² is constant for all planets going around the sun

Van Allen belts

two invisible, donut-shaped rings of high-energy charged particles—specifically protons and electrons—trapped by Earth's magnetic field

geostationary satellites

an Earth-orbiting satellite that matches Earth's rotation speed, stays positioned directly above the equator, and appears fixed motionless in the sky