Relative Velocity
Lecture 11
ME 231: Dynamics
Question of the Day
The velocity of the cart is
4 ft/s to the right.
Determine the angular
speed N (in rpm’s) of the
wheel so that point A on
the top of the rim has a
velocity equal to zero.
ME 231: Dynamics
Outline for Today
Question of the day
Relative velocity due to rotation
Interpretation of vA = vB + vA/B
Solution of relative-velocity equation
Answer your questions!
ME 231: Dynamics
Recall: Relative Motion
aA
rA
r?B rA / B
vA
r? A
rB r A / B
?v A
rA
rB rA / B
Absolute position of B is defined in an inertial
coordinate system X-Y
Attach a set of translating (non-rotating) axes x-y to
particle B and define the position of A
Define position of “A relative to
ME 231: Dynamics
B” (“A/B”) in x-y
Relative Velocity Due to Rotation
Movement in
two parts
First, body
translates
'rB to parallel
position
'rA 'rB 'rA / B
Second, body
rotates about From translating (non-rotating)
B’ through
axes x’-y’ attached to point B’,
the remaining motion is a simple
angle 'T
rotation about B’ giving 'rA/B
ME 231: Dynamics
Relative Velocity Due to Rotation
Relative velocity
as a scalar
vA/ B
lim
'rA / B
't
r'T
lim
't o0 't
rZ
't o0
…as a vector
v A/ B
ur
'rA
vA
v B v A/ B
ME 231: Dynamics
'rB 'rA / B
Dividing by 't
Interpretation of Relative-Velocity Equation
Translational
portion
Rotational
portion
90º
vB
vA
v B v A/ B
ME 231: Dynamics
v A/ B
ur
v A/ B
vA
vB
Outline for Today
Question of the day
Relative velocity due to rotation
Interpretation of vA = vB + vA/B
Solution of relative-velocity equation
Answer your questions!
ME 231: Dynamics
Solution of Relative-Velocity Equation: Case #1
Scalar-Geometric
v A2
2
A
v
vA
v A /O
rOZ
v A2 /O vO2 2v A /O vO cos120q
§vO ·
rO ¨ ¸ 2 m/s
© r ¹
2 3 223cos120q
4.36 m/s
v A/ O
2
2
2 m/s
vA
60º
r0
3 m/s
10 rad/s
ME 231: Dynamics
vO
vA
vO v A/ O
Solution of Relative-Velocity Equation: Case #2
Vector
vA
vA
vA
vO v A /O vO Z u r0
i
j
k
3i 0
0 10 3i 1.7 j i
0.17 0.1 0
v A/ O
4.36 m/s
v
4i 1.7 j m/s
A
r0
30º
3 m/s
10 rad/s
ME 231: Dynamics
vO
vA
vO v A/ O
Relative Velocity: Exercise
A mechanic “walks” a two-tire unit that rolls
without slipping at constant speed v. The radius
of both tires is r.
Determine the velocities
of points A, B, C, and D.
ME 231: Dynamics
Outline for Today
Question of the day
Relative velocity due to rotation
Interpretation of vA = vB + vA/B
Solution of relative-velocity equation
Answer your questions!
ME 231: Dynamics
For Next Time…
Complete Homework #4 due on
Thursday (9/20)
Read Chapter 6, Section 6.2
ME 231: Dynamics