Transcript What direction is this

Angular Mechanics - Vector cross product and
precession
Contents:
•Direction of angular velocity vector
•Torque and direction of torque
•Vector cross product | Whiteboard
•Now for something really stupid
•Now for something really wierd
Direction of angular velocity:
1. Wrap right hand
around the axis,
fingers in
direction of spin
2. Thumb is the
“direction” of 
Direction of angular velocity:
This  is in the
direction
.
Conventions:
. = Out of the page
x = Into the page
(Right hand threads)
What direction is this  ?
What direction is this  ?
What direction is this  ?
What direction is this  ?
What direction is this  ?
Vector Cross Product:
Torque is defined as
F
r
 = rxF
“x” in this case is the
vector cross product:
AxB = ABsin in the Rt hand direction
1. Take your right hand, and put your index finger in the
direction of the first vector. (r in this case)
2. Put your middle finger in the direction of the second. (F)
3. Your thumb is the direction of the cross product
4. Note that Vector x product is not commutative.
Vector Cross Product:
F
r
Note that this torque is
in the . direction (out
of the page) That
means it will cause an
angular acceleration in
the . direction! (Duh)
AxB = ABsin in the Rt hand direction
1. Take your right hand, and put your index finger in the
direction of the first vector.
2. Put your middle finger in the direction of the second.
3. Your thumb is the direction of the cross product
4. Note that Vector x product is not commutative.
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Find this cross product:
x
Precession
F
r
Concept 1
Ft = p = Impulse
t = L
Concept 2
p is in the direction of F
L is in the direction of 
Concept 3
The direction of  is funky!
Precession
r
Pivot Point
L
F(gravity)
Concept 4
Direction of L
Concept 5
Direction of rxF is x
Concept 6
The tip of the L vector
should change in direction
of torque!!!
Concept 7
This is precession!
Demo
Direction of Precession?
1. Find direction of L
2. Find torque direction
F
(rxF)
3. Tip of L vector will go
in the direction of torque
4. Simpler to apply force
to tip of L vector. Tail
Pivot Point moves in the opposite
direction of torque.
Direction of Precession?
1. Find direction of L
2. Find torque direction
F is x
3. Tip of L vector will go
in the direction of torque
4. Simpler to apply force
to tip of L vector. Tail
moves in the opposite
Pivot Point direction of torque.
Direction of Precession?
1. Find direction of L
2. Find torque direction
F is
3. Tip of L vector will go
in the direction of torque
4. Simpler to apply force
to tip of L vector. Tail
moves in the opposite
Pivot Point direction of torque.
.
Direction of Precession?
1. Find direction of L
2. Find torque direction
F is x
3. Tip of L vector will go
in the direction of torque
4. Simpler to apply force
to tip of L vector. Tail
moves in the opposite
Pivot Point direction of torque.