Unformatted text preview: Distribute the crossproduct, but keep the order the same
ˆ×ˆ = 0
ii
ˆ×ˆ = k
ijˆ
ˆ ˆ = −k
ˆ
j× i Fixed Axis Rotation
vω/ A =
r
B × y’ rB / A B/ A vB / A = rB / Aω aα/ A = × ω/ A +ω ×r ×
r
(
B
B
at = rB / Aα
an = rB / Aω 2 A B/ A ) vB
B
x’ Figure 7.2 Velocity
vector of point on body
in pure rotation about
fixed axis θ Fixed Axis Rotation
v B/ A =ω× r B/ A
aB/ A d
d
= ( vωA )r= (
B/ ×
dt
dt &
aB / A =ω× r B/ A ) +ω× r &B/ A
B/ A aB/ A =α× r B/ A+ω× v
aB/ A =α× r B/ A+ω×ω× r
( B/ A B/ A ) Planar simplification
aB/ A =α× r B/ A+ω×ω× r
( B/ A ) Fixed Axis Rotation in 2D
y’ v B/ A =ω× r B/ A rB / A vB / A = rB / Aω A aB/ A =α× r B/ A ω r B/ A an = rB / Aω 2 B
x’ Figure 7.2 Velocity
vector of point on body
in pure rotation about
fixed axis 2 at = rB / Aα vB
θ Special Case
If the angular acceleration of the body is constant, α = αC, the equations for angular velocity and acceleration can be integrated to yield the set of algebraic equations below. ω = ω0 + α C t
θ = θ 0 + ω0 t + 1 α C t 2
2
ω 2 = ω0 2 + 2α C ( θ − θ 0 )
θ0 and ω0 are...
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This document was uploaded on 04/01/2014.
 Spring '14

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