Mechanics Flashcards
Velocity
v = ds/dt
Acceleration
a = dv/dt
General Motion Formulas (4)
v =
x =
v2 =
v̅ =
v = v0 + at
x = x0 + v0t + ½at2
v2 = v02 + 2a(x − x0)
v̅ = ½(v + v0)
Newtons 2nd Law (2 Forms)
“Sum of the forces…”
∑ F = m a
∑ F = dp/dt
(p = momentum)
Weight
W = m g
Centripetal Acceleration (2 Forms)
ac = v2/r
ac= − ω2r
Momentum
p = m v
Efficiency
ℰ = Wout /Ein
Impulse
J = F̅ Δt
J =∫ F dt
Impulse–Momentum
F̅ Δt = m Δv
∫F dt = Δp
Work
- W* = F̅Δs cos θ
- W* = ∫F · ds
Work–Energy
F̅Δs cos θ = ΔE
∫F · ds = ΔE
Kinetic Energy (KE)
KE = ½mv2
Potential Energy (PE) (U)
ΔU = − ∫F · ds
Gravitational Potential Energy
ΔUg = mgΔh
Elastic Potential Energy
Us= ½kΔx2
Power
P̅ = F · v = F̅v cos θ
P̅ = ΔW / Δ*t = dW * / dt
Angular Velocity
ω̅ = Δθ/Δt = dθ/dt
v = ω × r
Angular Acceleration
α̅ = Δω/Δt = dω/dt
a = α × r − ω2 r
General Rotation Formulas (4)
ω =
θ =
ω2 =
ω̅ =
ω = ω0 + αt
θ = θ0 + ω0t + ½αt2
ω2= ω02 + 2α(θ − θ0)
ω̅ = ½(ω + ω0)
Newtons 2nd Law for Rotation (2 Forms)
“Sum of the torques…”
∑ τ = I α
∑ τ = dL/dt
(L = angular momentum)
Torque
τ = rF sin θ
τ = r × F
Moment of Inertia
I = ∑ mr2
I = ∫r2 dm
Parallel Axis Theorem
I = Icm + mh2
(h = distance between center of mass and pivot point)
Rotational Work
W = τ̅Δθ
W = ∫τ · dθ
Rotational Power
P = τ · ω
P = τω cos θ
Rotational Kinetic Energy
KE = ½Iω2
Angular Momentum
L = r × p
L = mrv sin θ
L = I ω
Frequency
ƒ = 1/T
ω = 2πƒ
Hooke’s Law
F = − k Δx
Universal Gravitation
