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2D Rigid Body Rotational Kinetics – Angular momentum
Angular momentum
L
:
–
For a point mass (particle):
L
=
m
υ
A
=
m
υ
r
sin
φ
=
m
υ
┴
r
A
: perpendicular distance from
O
(pivot) to the line of
υ
G
r
: distance from
O
(pivot) to the point mass
φ
: angle between
r
and
υ
υ
┴
: velocity component perpendicular to
r
–
For a rigid body in pure rotation:
L
=
I
ω
about pivot point
O
–
Direction of
L
: CW or CCW for 2D rotation
Newton’s 2nd law for 2D rigid body pure rotation
:
dL
dt
τ
Σ
=
Conservation of angular momentum
Σ
τ
= 0
→
L
i
=
L
f
or
L
1
=
L
2
Note: Collision involving a pivoted rigid body:
Conservation of momentum is
NOT
valid. Only
conservation of angular momentum is applicable.
Example
1. Two identical small spheres, each with mass 0.2 Kg, are mounted on a 0.8 Kg slender rod. The 0.9 m long
slender rod pivoted at its center rotates in a horizontal plane, and the spheres can slide along the rod. The slender
rod initially spins with an angular velocity of 30 rad/s when the spheres are 0.15 m from the center on each side.

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- Spring '08
- TSChang
- Physics, Angular Momentum, Kinetic Energy, Mass, Momentum, Rigid Body
-
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