12: Equations Flashcards
Angular velocity = (in terms of angle)
ω = θ/t
θ = angle (radians)
Linear Velocity = (in terms of ω)
v = rω
v = linear velocity
ω = angular velocity
r = radius
another equation for angular velocity regarding the circumference of the circle in radians
circumference / time taken for one revolution
ω = 2* π * f (frequency)
how can we write linear velocity using the equation for angular velocity (circumference)
v = 2πrf
equation for centripetal acceleration using linear velocity
a = v^2 r
equation for centripetal acceleration angular velocity
a = ω^2 r
equations for centripetal acceleration using linear velocity and angular velocity
f = m a
where a = v^2 / r
so f =mv^2 / r
a = ω^2 * r
so f = ma = mω^2 * r
break down the equation of gravitational force F = − GMm / R^2
what does the negative sign mean
F = gravitational force
M = mass of bigger object
m = mass of smaller object
G = gravity force constant
R = distance of m from M (or radius)
the negative sign shows that Fgrav is in the opposite direction to the displacement of m from M
what is the equation g = GM / r^2 for
units
gravitational field strength
N / Kg
what is the equation -GMm / r for
gravitational potential energy
what is the equation -GM / r for
define it
gravitational potential
its the energy per unit mass for a single object
what energy does a spacecraft need to make it out of earth’s potential well
use this to find escape velocity
Ekinetic + Epotential >= 0
1/2mv² + (-)GMm/r >= 0
Vesc = SQR (2GM / r)