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Unformatted text preview: Summary Lecture 16
Rotational and Linear Motion
and Linear Motion
Displacement
Linear:
Rotational: Conversion:
Arclength l: Velocity Δx, measured in [m]
Δθ, difference in angle
difference in angle
measured in [rad]
360 degrees = 2π rad
θ[rad] = θ[degrees] *2π/360
*2
l = θ r; θ in [rad] Linear:
Rotational: v = Δx/Δt, measured in [m/s]
ω = Δθ/Δt, measured in [rad/s] Period
Frequency T = time for one revolution
f = # of revs per second
f = 1/T
ω = 2π/T = 2πf Acceleration
Linear:
Rotational: a = Δv/Δt, measured in [m/s2]
α = Δθ/Δt; measured in [rad/s2] Uniformly Accelerated Motion:
(constant acceleration) Linear
v = v0+at
x = x0+v0t+1/2at2
v2 = v02+2aΔx
v = (v+v0)/2 Rotational
ω = ω 0 + αt
θ = θ0+ω0t+1/2αt2
ω2= ω02 + 2αΔθ
ω = (ω + ω0)/2
+ centripetal acceleration
ac = v2/r = ω2r The Object vs. Individual Points
Frequency, period, angular velocity
and angular acceleration are properties
of the body as whole
of the body as a whole,
i.e. every point moves with the same
angular velocity. (T, f, ω, α)
Each individual point also has a linear
velocity, a linear acceleration and as
always in circular motion a centripetal
acceleration:
vT = Δx/Δt = 2πr/T = ωr
a T = Δ v /Δ t = Δ ω /Δ t r = α r
aC = vT2/r = ω2 r ...
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This note was uploaded on 12/06/2011 for the course PHYSICS 111&112 taught by Professor Unknown during the Spring '11 term at Ohio State.
 Spring '11
 UNKNOWN

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