Rotational Motion Flashcards
ω̄ (average angular velocity) =
Δθ/Δt
ω (instantaneous angular velocity) =
dθ/dt
ᾱ (average angular acceleration) =
Δω/Δt
α (instantaneous angular acceleration) =
dω/dt
Define a rigid body
All points along a radial line always have the same angular displacement.
Δθ (angular displacement) =
Δs/r
s = arc length
v̄ (average linear velocity) =
rω̄
v (instantaneous linear velocity) =
rω
a (instantaneous linear acceleration ) =
rα
ac (instantaneous centripetal acceleration) =
(v^2)/r = (ω^2)r
Big Five #1:
Δθ =
ω̄ t
Big Five #2
ω =
ω0 + αt
Big Five #3
θ =
θ0 + ω0t + 0.5α(t^2)
Big Five #4
Δθ =
ωt - 0.5α(t^2)
Big Five #5
(ω^2) =
(ω0^2) + 2αΔθ
τ (torque) =
rFSin(θ)
(θ is the angle between the extension of r and the direction of F)
lF
(l is the component of r that is perpendicular to F)
τ̂ (torque) =
r̂ x F̂
Pulley Tension Force and Torque
τ (torque) =
rF
τ (torque) =
m(r^2)α
Rotational Inertia or Moment of Inertia
I =
∫(r^2)dm
Στ = `
Iα
l is moment of inertia
Rotational
KE =
0.5I(ω^2)
Rolling
KE =
0.5 *I *(ω^2) + 0.5m(v^2)
