statics, gravity, and shm

conditions for static equilibrium

net force is zero, torque is zero

center of gravity

gravitational force on a body effectively acting on a single point

• if g is the same for all elements of the body, then the body’s center of gravity is coincident with the body’s center of mass.

center of gravity equation

newton’s law of universal gravitation

G = 6.67 × 10^-11 Nm²/kg²

Kepler’s First Law

All plants move in elliptical orbits with the sun at one focus

perihelion - closest to the sun

aphelion - farthest from the sun

Kepler’s Second Law

a line joining any planet to the sun sweeps out equal areas in equal times

Kepler’s Third Law

The square of the period of any planet is proportional to the cube of the semimajor axis of orbit

semimajor axis ½ of major axis

Kepler’s Third Law equations

T²=kr³

gravitational potential energy

due to an object’s location from the center of the Earth

kinetic energy

k = 1/2mv²

k = -U/2


Etotal = U + K = U/2

simple harmonics motion

refers to the motion an oscillating mass experiences when the restoring force is proportional to the displacement, but in opposite directions.

• represented by sine/cosine wave

• constant frequency and amplitude

SHM equations

T = 1/f;

angular frequency equations

shm position graph and equation

x(t) = A cos (ωt)

shm velocity graph and equation

V(t) = -Aωsin(ωt)

Vmax = Aω = 2pi/T = A2pi*f

shm acceleration graph and equation

a(t) = -Aω²cos(ωt)

Amax = Aω² = A4pi²/T² = A4pi²f²

SHM Energy equations

shm chart