12: Equations Flashcards

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1
Q

Angular velocity = (in terms of angle)

A
ω = θ/t
θ = angle (radians)
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2
Q

Linear Velocity = (in terms of ω)

A

v = rω

v = linear velocity
ω = angular velocity
r = radius
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3
Q

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

A

circumference / time taken for one revolution

ω = 2* π * f (frequency)

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4
Q

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

A

v = 2πrf

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5
Q

equation for centripetal acceleration using linear velocity

A

a = v^2 r

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6
Q

equation for centripetal acceleration angular velocity

A

a = ω^2 r

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7
Q

equations for centripetal acceleration using linear velocity and angular velocity

A

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

a = ω^2 * r
so f = ma = mω^2 * r

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8
Q

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

A
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
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9
Q

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

units

A

gravitational field strength

N / Kg

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10
Q

what is the equation -GMm / r for

A

gravitational potential energy

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11
Q

what is the equation -GM / r for

define it

A

gravitational potential

its the energy per unit mass for a single object

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12
Q

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

use this to find escape velocity

A

Ekinetic + Epotential >= 0

1/2mv² + (-)GMm/r >= 0

Vesc = SQR (2GM / r)

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