# znotes Flashcards

Radian

One radian is the angle subtended from the center of the circle by an arc length equal to the radius of the circle

Angular displacement

The angle through which an object has moved through a circle

Angular velocity

The rate of change of the angular position of an object as it moves along a curved path

ω= θ / t

ω= 2π / T = 2πf

Linear velocity

v = ωr

Centripetal force

Resultant force acting on an object perpendicular to its linear velocity towards the center of the circle. Causes circular motion.

F= mv^2 / r = mrω^2

Centripetal acceleration

Derived by equating Newton’s 2nd law and centripetal force

ma = mrω^2 a = rω^2 = v^2/r

Gravitational field strength

The force experienced per unit mass at a point in the gravitational field

g= GM/r^2

Newton’s law of gravitation

The gravitational force present between two masses is directly proportional to the product of the two masses and inversely proportional to the square of their separation.

F = GMm/r^2

Gravitational potential

The work done per unit mass in bringing a point mass from infinity to a point in the gravitational field

ϕ = −GM/r

Gravitational potential is negative because its maximum value is 0 at infinite distance away from the mass

gpe = mgh can be used on Earth’s surface

Gravitational potential energy

The work done in bringing a point mass from infinity to a point in the gravitational field

U = mϕ = −GMm/r

Centripetal acceleration

For an orbiting satellite the cnetripetal force is provided by the gravitational field

GMm/r^2 = mv^2/r v^2 = GM / r

Geostationary orbit

It is always above a fixed point on the equator of the Earth

Fixed period of 24hrs

Moves from West to East - same direction as Earth

Escape velocity of a satellite

Initial KE + Initial GPE = 0

1/2mv^2 = GMm/r

v = (2GM/r)^ 1/2

Avogadro constant

Number of molecules present in 12g of carbon-12

Ideal gas

A gas which obeys the ideal gas equation for all temperatures, pressures and volumes.

pV = nRT

where R = 8.31