12: Equations

Question 1

Angular velocity = (in terms of angle)

Answer 1

ω = θ/t
θ = angle (radians)

Question 2

Linear Velocity = (in terms of ω)

Answer 2

v = rω

v = linear velocity
ω = angular velocity
r = radius

Question 3

another equation for angular velocity regarding the circumference of the circle in radians

Answer 3

circumference / time taken for one revolution
ω = 2* π * f (frequency)

Question 4

how can we write linear velocity using the equation for angular velocity (circumference)

Answer 4

v = 2πrf

Question 5

equation for centripetal acceleration using linear velocity

Answer 5

a = v^2 r

Question 6

equation for centripetal acceleration angular velocity

Answer 6

a = ω^2 r

Question 7

equations for centripetal acceleration using linear velocity and angular velocity

Answer 7

f = m a
where a = v^2 / r
so f =mv^2 / r

a = ω^2 * r
so f = ma = mω^2 * r

Question 8

break down the equation of gravitational force F = − GMm / R^2
what does the negative sign mean

Answer 8

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

Question 9

what is the equation g = GM / r^2 for
units

Answer 9

gravitational field strength
N / Kg

Question 10

what is the equation -GMm / r for

Answer 10

gravitational potential energy

Question 11

what is the equation -GM / r for
define it

Answer 11

gravitational potential
its the energy per unit mass for a single object

Question 12

what energy does a spacecraft need to make it out of earth’s potential well

use this to find escape velocity

Answer 12

Ekinetic + Epotential >= 0

1/2mv² + (-)GMm/r >= 0

Vesc = SQR (2GM / r)