Angular Momentum of circular disk

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SUMMARY

The discussion focuses on calculating the angular momentum and resulting angular speed of a flat uniform circular disk with a radius of 2.50 m and mass of 100 kg, when a 55.0 kg person runs on it at a tangential speed of 2.20 m/s. The key equations involved are the angular momentum equation (L = I * ω) and the moment of inertia formula (I = m * r²). The initial angular momentum of the system is zero since the disk is stationary. The conservation of angular momentum principle is crucial for determining the final angular speed after the person begins to run.

PREREQUISITES
  • Understanding of angular momentum and its conservation
  • Familiarity with moment of inertia calculations
  • Knowledge of rotational motion equations
  • Basic physics concepts related to circular motion
NEXT STEPS
  • Calculate the moment of inertia for the disk using I = m * r²
  • Explore the conservation of angular momentum in rotating systems
  • Learn how to derive angular speed (ω) from angular momentum (L)
  • Investigate real-world applications of angular momentum in engineering
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Students studying physics, particularly those focusing on rotational dynamics, as well as educators looking for practical examples of angular momentum in action.

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Homework Statement


A flat uniform circular disk (radius = 2.50 m, mass = 1.00 102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 55.0 kg person, standing 1.55 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.20 m/s relative to the ground.


Homework Equations



I have been using the definition of angular motion equation (L = I*omega)(I = mr^2) to try and find the resulting angular speed. What I am having trouble with is how to find L using the given numbers. I thought i read that L = r2, but putting those numbers into the equation has not given me the correct answer. The problem asks me to find the resulting angular speed, but since I have not been able to find L or omega, I haven't been able to solve.

Thanks.
 
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Hint: Angular momentum is conserved. What's the initial angular momentum of the system before the person begins running?
 

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