# 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 = 2π*r*f

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)