LECTURE 25
CONSERVATION OF ANGULAR MOMENTUM
Instructor: Kazumi Tolich
Lecture 25
2
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Reading chapter 11-7
¤
Conservation angular momentum
Conservation of angular momentum
3
¨
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
Helicopter
4
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Why does a helicopter have a second small rotor fixed close to its tail?
¤
Without the small rotor, to conserve angular momentum of the helicopter, when
the blades of the main rotor rotate, the helicopter’s body rotates in the
opposite way. The tail rotor produces a torque that stops the rotational motion
of the helicopter’s body.
Demo: 1
5
¨
Stool and bicycle wheel
¤ Demonstration
momentum
of conservation of angular momentum and sign of angular
Cats conserve angular momentum!
6
A cat usually lands on its feet regardless of the
position from which it is dropped.
¨ A slow-motion film of a cat falling shows that the
upper half of its body twists in one direction while
the lower half twists in the opposite direction.
¨ The total angular momentum of the cat remains
zero.
¨
Example: 1
7
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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
9
¨
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
Demo 2
10
¨
Marbles and Funnel
¤ Demonstration
of conservation of angular momentum
¤ Centripetal force and tangential velocity
𝐍
𝐍
𝐖
Side View
𝐯
Top View
Quiz: 2 through 5
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