Rod swinging and hitting a ball

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Homework Help Overview

The problem involves a uniform rod and a ball, where the rod swings down from a fixed position and collides with the ball. The goal is to find the angular velocity of the rod before and after the collision, as well as the translational and angular speeds of the ball after the collision. The context includes concepts from dynamics and rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of energy conservation to find the initial angular velocity of the rod and the application of angular momentum conservation during the collision. There are questions about the assumptions regarding the nature of the collision (elastic vs. inelastic) and the implications of friction on the ball's motion.

Discussion Status

Participants are exploring various interpretations of the collision dynamics, including the effects of friction and the nature of the impact. Some guidance has been offered regarding the need for additional equations to account for different forces acting during the collision, but no consensus has been reached on the approach to take.

Contextual Notes

There are discussions about the assumptions made regarding the collision process, including the time scale of the impact and the role of friction. The participants also note the importance of defining the axes for calculating moments of inertia and the velocities involved in the collision.

  • #31
erfz said:
@haruspex
I'm thinking now, would it be possible to set your axis on the table that the ball sits on and treat the rod and ball as a single system?
This would eliminate frictional torque, I think.
Do you see anything wrong with that?
But then you would have torque from the unknown reaction at the rod's hinge.
You can take anywhere as your reference points for angular momentum, but if that means dragging in the reaction force from the hinge or the friction from the table then you will need to bring in a linear momentum equation as well in order to eliminate the unknown. The great benefit of using the rod's axis for its equation and the point of contact of the ball with the table for its equation is that we never get those impulses in the equations.
 
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  • #32
haruspex said:
But then you would have torque from the unknown reaction at the rod's hinge.
You can take anywhere as your reference points for angular momentum, but if that means dragging in the reaction force from the hinge or the friction from the table then you will need to bring in a linear momentum equation as well in order to eliminate the unknown. The great benefit of using the rod's axis for its equation and the point of contact of the ball with the table for its equation is that we never get those impulses in the equations.
Ah, shoot. I forgot about that completely. Thank you very much!
 

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