Angular Momentum and collisions w/o friction

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SUMMARY

The discussion focuses on a physics problem involving a bicycle wheel and a dart, specifically analyzing angular momentum and collisions without friction. The key equations referenced include ωr = v and the moment of inertia formula, I = MR². Participants seek clarification on calculating the angular momentum of the dart before impact and the moment of inertia for the combined system post-collision. The problem requires understanding the relationship between linear and angular momentum in a rotational system.

PREREQUISITES
  • Understanding of angular momentum and its calculation
  • Familiarity with moment of inertia concepts
  • Knowledge of rotational dynamics and equations of motion
  • Basic principles of collisions in physics
NEXT STEPS
  • Study the calculation of angular momentum in rotating systems
  • Learn about moment of inertia for various shapes and systems
  • Explore the principles of conservation of angular momentum
  • Investigate the effects of inelastic collisions in rotational motion
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Students studying physics, particularly those focusing on mechanics, as well as educators and tutors looking for examples of angular momentum and collision problems.

Ric
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Homework Statement


A bicycle wheel of mass M (assumed to be concentrated at its rim) and radius R is mounted horizontally so it may turn without friction on a vertical axle. A dart of mass m0 is thrown with velocity v0 as shown above and sticks in the tire. ( A top-view is shown to the right.)
a. What is the angular momentum of the dart about the wheel's center just before the dart strikes the rim of the wheel?
b. What is the moment of inertia of the dart and wheel system?
c. How long will it take for the wheel to make on full rotation after the collision happens?

Homework Equations


ωr=v
M R02

The Attempt at a Solution


Is (a) just the linear momentum of the dart multiplied by the radius?
 
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I don't see the picture. In what way does the dart strike the tyre?
 

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