Physics 2211a Kulp Class 44: What changes angular momentum

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Physics 2211a (Kulp)Class 44 What changes
angular momentum?
Final exam Period 15 (250 - 540 PM, 15
Dec) L2 -gt L2 N113/S105 -gt Boggs B6A

• W. D. Kulp
• william.kulp at physics.gatech.edu
• Office W501b
• Office Hours MF 11-12 AM, Tu 9-10 AM, by appt.
• www.physics.gatech.edu/academics/Classes/fall200
  6/2211/a/

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Where were we?

• Last class (Energy, constraints)

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• A solid disk and a ring roll down an incline.
• The ring is slower than the disk if

• mring mdisk, where m is the inertial mass
• rring rdisk, where r is the radius
• mring mdisk and rring rdisk
• The ring is always slower.

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Where are we?

• Last class (Energy, constraints)

• Today Class 44
• Calculate the cross product of two given vectors.
• Given vector representations for applied forces
  and moment arms, calculate the torque on an
  object and analyze the motion of the object.
• Use conservation of angular momentum to analyze
  the motion of a rigid body.

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Direction of torque

• Up to this point, we have described the direction
  of torques as CCW () or CW (-).

Clockwise (-)
Counter-clockwise ()
F

• This is problematic if two observers cannot agree
  on the which way an object is rotating!
• Need to define direction in consistent vector
  notation.

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Torque as a cross product

• The right-hand rule thumb points in direction
  of the cross product.

• Vector order is important!

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Cross Product Algebra

• Properties

• Math trick determinant

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Angular Momentum

• For a particle
• For a rigid body

• If there is no net torque, angular momentum is
  conserved.

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Conservation of angular momentum

• Colliding and sticking moving masses

M
M
m
m
v1
v2
V

• Colliding and sticking rotating masses

?1
?2
?
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Going for a spin

• A boy of mass 40 kg runs to a merry-go-round of
  radius 2.0 m and mass 100 kg and jumps on to the
  outer edge at 10 m/s. What is the resulting ??

• (200)(0) (160)(5) (200 160) ?
• ? 2.22 rad/s

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Is he dizzy?

• After jumping on the merry-go-round, the boy
  moves to a position 0.5 m from its center.
• What is the speed of the boy?

• (160 200)(2.22) (10 200) ?
• 3.81 rad/s
• vbf r? (0.5)(3.81) 1.9 m/s

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Going for another spin

• A boy of mass 40 kg runs to a merry-go-round of
  radius 2.0 m and mass 100 kg and jumps on to the
  outer edge at 10 m/s.
• What is change in kinetic energy?

• 2000 -887
• 1113 J

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Working for it

• After jumping on the merry-go-round, the boy
  moves to a position 0.5 m from its center.
• How much work does this move require?

• 1524 - 887
• 637 J

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• The angular momentum L(t) of a particle in four
  situations is given below
• L 3t 4
• L -6t2
• L 2
• L 4/t

• In which situation is the net torque on the
  particle
• Zero
• Positive and constant
• Negative and increasing in magnitude
• Negative and decreasing in magnitude

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Physical pendulum
pivot

• A pendulum is formed by attaching a hollow sphere
  (m1 9.0 kg, r 0.20 m) to the end of a thin
  rod (m2 9.0 kg, l 0.30 m). The pendulum
  pivots about one end of the rod

• What is the moment of inertia?

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Physical pendulum

• A pendulum is formed by attaching a hollow sphere
  (m1 9.0 kg, r 0.20 m) to the end of a thin
  rod (m2 9.0 kg, l 0.30 m). The pendulum
  pivots about one end of the rod

• If this pendulum is displaced from equilibrium,
  what is the period of oscillation?

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Whats next?

• Friday, 12/8 Class 45 Conclusion What have we
  learned?
• Advice for the Final Exam.
• Diagnostic comparison test - for extra credit!

• To-do list
• Assignment 40 due before class on Friday.
• Please fill out the electronic course evaluation