Ch. 5 - 8 Flashcards
Work done on an object
W = FxΔx W = (Fcosθ)d
Frictional Work
W= -μnΔx
Kinetic Energy
1/2mv^2
W(net)
ΔKE
Gravitational Potential Energy
PE = mgy
Work due to non-conservative forces
Wnc = ΔKE + ΔPE
setting Wnc = 0
KEi+PEi=KEf+PEf
Spring Potential Energy
PEs = 1/2kx^2
Power
P = W/Δt = Fv
Linear momentum
p = mv
Fnet (in terms of momentum)
F = Δp/Δt
Impulse
I = FΔt = mvf - mvi
Conservation of Momentum
m1v1i + m2v2i = m1v1f + m2v2f
Perfectly Inelastic Collisions
m1v1i +m2v2i = (m1 + m2)vf
Elastic Collisions
1/2m1v1i^2 + 1/2m2v2i^2 = 1/2m1v1f^2 +1/2m2v2f^2
v1i - v2i = -(v1f - v2f)
Thrust of Rocket
v(exhaust)(∆M/∆t)
Velocity of Rocket
vf-vi = v(exhaust)(Mi/Mf)
Relation between angle and arc length
θ = s/r s = displacement along circular arc r = radius
Angular Displacement
∆θ = θf - θi
Average Angular Speed
ω = ∆θ/∆t
Average Angular Acceleration
α = ∆ ω/∆t
Linear Tangential Speed of a Particle Moving in a circular path
vt = r ω r = radius
Tangential Acceleration
at=∆αr
Centripetal Acceleration
ac = v^2/r ac = r ω^2
Total Acceleration in Rotation
a = √at^2 + ac^2
Centripetal Force
Fc = m(v^2/r)
Newton’s Law of Universal Gravitation
F = G (m1m2/r^2)
Gravitational Potential Energy
PE = -G (Mem/r)
Escape Speed
v(esc)=√2GMe/Re
Period of a planet in orbit
T^2 = (4π^2/GMs)r^3
Torque
τ=rFsinθ
τ = rF
r = length of the position vector (x)
Torque and Two Conditions for Equilibrium
summation of F = 0
summation of τ = 0
center of gravity
x (cg) = summation of (mixi/mi)
y (cg) = summation of (miyi/mi)
Torque acting on an object about an angle of rotation
τ = mr^2α τ = Iα
Inertia
I = summation of mr^2
Rotational Kinetic Energy
KE = 1/2 I ω^2
Angular Momentum
L = I ω
Tau in terms of Momentum
summation of τ=∆L/∆t
Conservation of Angular Momentum
Li = Lf Iiωi = Ifωf
Rotational Motion under Constant Angular Acceleration
ω = ωi + at ∆θ = ωit + 1/2at^2 ω^2 = ωi^2 + 2a∆θ