Angular Mechanics Vector cross product and precession Contents

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 = rx. F “x” in this case is the vector cross product: Ax. B = 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) Ax. B = 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 rx. F 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 (rx. F) 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.