cm + gravity

Question 1

equation for arc length (s)? (r, θ)

Answer 1

s = rθ

Question 2

equation for angular velocity (ω)? (θ, t)

Answer 2

ω = θ/t

(or more accurately, ω = dθ/dt)

Question 3

equation for period (T) of rotation? (ω)

Answer 3

ω = 2π/T

(found by period = total angle in one rotation/angular velocity)

Question 4

equation for frequency (f) of rotation? (ω)

Answer 4

ω = 2πf

Question 5

equation for linear velocity (v)? (r, ω)

Answer 5

v = rω

Question 6

equation for centripetal acceleration (a)? (v, ω)

Answer 6

a = vω

Question 7

equation for centripetal acceleration (a)? (ω, r)

Answer 7

a = (ω^2)r

Question 8

equation for centripetal acceleration (a)? (v, r)

Answer 8

a = (v^2)/r

Question 9

equation for centripetal force (F)? (m, v, ω)

Answer 9

F = mvω

Question 10

equation for centripetal force (F)? (m, ω, r)

Answer 10

F = m(ω^2)r

Question 11

equation for centripetal force (F)? (m, v, r)

Answer 11

F =[m(v^2)]/r

Question 12

equation for gravitaional field strength (g)? (F, m)

Answer 12

g = F/m

where F = gravitational force

Question 13

equation for gravitational force (F)? (M, m, r)

Answer 13

F = - (GMm)/(r^2)

where G = universal gravitational constant, M = mass of body being orbited, m = mass of orbiting body, r = distance between centres of each body

(minus sign bc gravitational force is attractive force [think opposites attract])

Question 14

equation for linear velocity? (G, M, r)

Answer 14

v = √[(GM)/r]

Question 15

‘equation’ for kepler’s third law? (T, r)

Answer 15

(time period of orbit)^2 ∝ (distance of planet from star or radius of orbit)^3

T^2 ∝ r^3

T^2 = [(4π^2)/GM]r^3

Question 16

equation for orbital [linear] velocity? (r, T)

Answer 16

v = 2πr/T

Question 17

equation for escape velocity? (M, r)

Answer 17

v = √[(2GM)/r]

(or v = √2V where v = gravitational potential?)

Question 18

equation for gravitational field strength (g)? (M, r)

Answer 18

g = -(GM)/(r^2)

Question 19

equation for gravitational potential energy (GPE) [in uniform field]? (m, V)

Answer 19

ΔGPE = mΔV

where V = gravitational potential

Question 20

equation for gravitational potential (V) in uniform field? (g, r)

Answer 20

V = gr

where g = gravitational field strength

Question 21

equation for gravitational potential (V)? (M, r)

Answer 21

V = -(GM)/r

Question 22

equation for gravitational potential energy (GPE)? (M, m, r)

Answer 22

GPE = -(GMm)/r

Question 23

equation for ΔGPE? (m, g, h)

Answer 23

ΔGPE = mgΔh

Question 24

equation for ΔV? (g, h)

Answer 24

ΔV = gΔh

Question 25

how are F, GPE, g and V linked?

Answer 25

Question 26

equation for total mechanical energy?

Answer 26

total mechanical energy = PE + KE

Question 27

what is total internal energy of system?

Answer 27

total internal energy in system = total PE of particles in system + total KE of particles in system