Angular Momentum and collisions w/o friction

AI Thread Summary
The discussion focuses on a physics problem involving a bicycle wheel and a dart, specifically calculating the angular momentum of the dart before impact, the moment of inertia of the combined system, and the time for the wheel to complete one rotation post-collision. Participants express confusion about the relationship between linear momentum and angular momentum, particularly how to compute the angular momentum of the dart relative to the wheel's center. There is also uncertainty regarding the dart's trajectory and the nature of its impact with the wheel. Clarifications on these points are sought to facilitate solving the problem effectively. Understanding the mechanics of angular momentum in this context is crucial for accurate calculations.
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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?
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
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