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ANGULAR KINETICS (continuation)
Moment of inertia
In angular kinetics (i.e., for rotation), inertia is represented by the moment of inertia of
the body.
(Think of “moment-of-inertia” as a long word meaning “difficult to get rotating, and once
it has started rotating, difficult to stop”; don’t think of is as “the moment of the inertia”.)
Definition of moment of inertia: I =
# m" r
2
!
Units for moment of inertia: kilogram ⋅ meter2
(Kg ⋅ m2)
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Angular momentum
Angular momentum = H = I ⋅ ω
← parallel concept to:
Units for angular momentum: kilogram ⋅ meter2 / second
linear momentum = m ⋅ v
(Kg ⋅ m2 / s)
Angular momentum (H) is a vector, same direction as the angular velocity (ω)
Newton’s angular laws
Parallelism with Newton’s “linear” laws
Newton’s 1st Angular Law. A body will rotate with constant angular momentum
unless an external torque is exerted on it.
= “Principle of conservation of angular momentum”
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Newton’s 2nd Angular Law. If you apply a torque on a body, the body will experience
an angular acceleration. The larger the torque, the larger the angular acceleration;
the larger the moment of inertia, the smaller the angular acceleration.
α=
T
I
← parallel concept to: a =
!
F
m
!
Another form of Newton’s 2nd Angular Law:
T⋅t=ΔI⋅ω
← parallel concept to:
angular impulse = Δ angular momentum
F⋅t=Δm⋅v
linear impulse = Δ linear momentum
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In the air, angular momentum = constant.
Need to get appropriate angular momentum before leaving the ground.
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Newton’s 3rd Angular Law. If one system exerts a torque on another system, the
second system will exert an equal and opposite torque on the first.
“Action and reaction torques”
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Some conclusions
In a jump:
Parabola of c.m. is fixed
... although one body part can go up if another part goes down.
Angular momentum is fixed
... although you still can:
 change
moment of inertia (I) to change angular velocity (ω)
 action-and-reaction
rotations
In most jumps, actions in the air are much less important than actions on the ground (runup and takeoff).
In other jumps, actions in the air are as important as actions on the ground.