11.1 Angular Momentum
translational angular
momentum
spin angular
momentum
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Angular Momentum - Engineering Physics - Lecture Slides, Slides of Engineering Physics
Here you can find a complete lecture series on Engineering Physics course. These lecture slides includes: Angular Momentum Principle, Velocities, Rotational Kinetic Energies, Energy Conservation, Torque, Nonzero, Horizontal Axle
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2013/2014
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11.1 Angular Momentum
translational angular
momentum
spin angular
momentum
11.1 Angular Momentum
translational angular
momentum
spin angular
momentum
11.1 Vector Cross Product
r × p = det
xˆ yˆ zˆ
r x
r y
r z
p x
p y
p z
r × p = r y
p z
− r z
p y
, −(r x
p z
− r z
p x
), r x
p y
− r y
p x
L = r × p = |r||p| sin θ
11.1 Vector Cross Product
r × p = det
xˆ yˆ zˆ
r x
r y
r z
p x
p y
p z
r × p = r y
p z
− r z
p y
, −(r x
p z
− r z
p x
), r x
p y
− r y
p x
L = r × p = |r||p| sin θ
11.1 Vector Cross Product
r × p = det
xˆ yˆ zˆ
r x
r y
r z
p x
p y
p z
r × p = r y
p z
− r z
p y
, −(r x
p z
− r z
p x
), r x
p y
− r y
p x
L = r × p = |r||p| sin θ
vector 1
vector 2
11.1 Vector Products
A · B = |A||B| cos θ
A × B = |A||B| sin θ
dot product
SCALAR
cross product
vector 1
vector 2
VECTOR
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p = <3,0,4> kg m s
- and r A
= <0,2,-6> m ,
What is the dot product of r A
and L?
(A) 4.9 (B) 0 (C) 22.1 (D) -24 (E) 17.
What is the angle between r A
and L (in degrees)?
(A) 36.6 (B) 40.6 (C) 42.4 (D) 90 (E) 45
What is the dot product of p and L?
(A) -17 (B) 0 (C) 22.1 (D) -24 (E) 12
What is the angle between p and L (in degrees)?
(A) 14.1 (B) 36 (C) 42.4 (D) 90 (E) 45
Clicker Quiz
p = <3,0,4> kg m s
- and r A
= <0,2,-6> m ,
What is the dot product of r A
and L?
(A) 4.9 (B) 0 (C) 22.1 (D) -24 (E) 17.
What is the angle between r A
and L (in degrees)?
(A) 36.6 (B) 40.6 (C) 42.4 (D) 90 (E) 45
What is the dot product of r A
and L?
(A) -17 (B) 0 (C) 22.1 (D) -24 (E) 12
What is the angle between r A
and L (in degrees)?
(A) 14.1 (B) 36 (C) 42.4 (D) 90 (E) 45
Clicker Quiz
11.1 Direction of Angular Momentum
L
trans
| = | r|| p| sin θ
L
trans
≡ r × p
Right-hand rule for cross products
11.1 Direction of Angular Momentum
L
trans
| = | r|| p| sin θ
L
trans
≡ r × p
Clicker Quiz
Q11.1.m: If an object is traveling at a constant speed in a vertical circle, how does
the object's angular momentum change as the object goes from the top of the circle
to the bottom of the circle?
11.1 Perpendicular Distance
Calculating Angular Momentum
Use three different methods to calculate the angular momentum of the
particle in the Figure relative to location B. How does this value compare to
the angular momentum of the same particle relative to location A and to
location C?
11.1 Angular Momentum Example
11.2 Rotational Angular Momentum
What is the rotational angular
momentum of a multi-
particle system?