LECTURE 25
CONSERVATION OF ANGULAR MOMENTUM
Instructor: Kazumi Tolich
Lecture 25
2
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Reading chapter 11-7
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Conservation angular momentum
Conservation of angular momentum/Demo: 1
3
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The law of conservation of angular momentum states
When the net external torque acting on a system about some axis remains zero, the
total angular momentum of the system about that axis is constant.
If ∑ 𝜏 = 0, ∑ 𝜏 =
¨
¨
¨
∆'
∆(
=0
The law of conservation of angular momentum is one of the most important laws of
nature along with conservations of energy and linear momentum.
http://www.youtube.com/watch?v=AQLtcEAG9v0
Demo: Stool and bicycle wheel
Examples of angular momentum conservation/Demo: 2
4
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Small rotor close to the tail of a helicopter
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The eye of a hurricane
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Falling cats
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As the rotating air is drawn towards the center, the
moment of inertia decreases, and the speed increases.
the upper half of its body twists in one direction while
the lower half twists in the opposite direction.
Demo: Marbles and Funnel
𝐍*+
𝐍*+
𝐖*Side View
𝐯
Top View
Example: 1
5
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A child of mass m stands at rest near the
rim of a stationary merry-go-round of
radius 𝑅 and moment of inertia 𝐼. The child
now begins to walk around the
circumference of the merry-go-round with a
tangential speed 𝑣 with respect to the
merry-go-round’s surface.
a)
b)
What is the child’s speed with respect to
the ground?
Check the result in limits where 𝐼
approaches 0, and 𝐼 approaches ∞.
Quiz: 1
Example: 2
7
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A uniform thin rod of length 𝑙 = 0.50 m and mass
𝑀 = 4.0 kg can rotate in a horizontal plane
about a vertical axis through its center. The rod is
at rest when a bullet with a mass 𝑚 = 3.0 g
traveling in the horizontal plane of the rod is
fired into one end of the rod. As viewed from
above, the direction of the bullet’s velocity makes
an angle of 𝜃 = 60.0º with the rod. If the bullet
lodges in the rod, and the angular velocity of the
rod is 𝜔 = 10.0 rad/s immediately after the
collision, what is the magnitude of the bullet’s
velocity just before impact?
Axis
𝜃 = 60.0º
Quiz: 2 through 5
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