Question about centre of percussion of a baseball bat

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Homework Help Overview

The discussion revolves around the concept of the center of percussion of a baseball bat, particularly focusing on the relationship between linear and angular velocities during motion. Participants are exploring the dynamics involved when a bat strikes an object and the implications of various pivot points.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are questioning how changes in angular velocity can coexist with no change in linear velocity. There are attempts to express relationships between linear and angular quantities, with some participants expressing confusion over specific terms and equations used.

Discussion Status

The discussion is active, with participants providing insights and questioning each other's reasoning. Some have offered guidance on the use of reference frames, while others are clarifying definitions and relationships between variables. There is a mix of interpretations being explored, particularly regarding the definitions of axes and the implications of using different frames of reference.

Contextual Notes

Participants are navigating through the complexities of angular momentum and the definitions of various parameters, such as the rotational pivot and the center of mass frame. There is an emphasis on ensuring that the chosen axis aligns with the definitions provided in the context of the problem.

Clara Chung
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Homework Statement


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The Attempt at a Solution


I don't know how to do the last part. How can there be no change in velocity of there is a change in angular velocity of the bat? Is the grip point acting as another axis?
 

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Clara Chung said:
How can there be no change in velocity of there is a change in angular velocity of the bat?
If the linear velocity of the mass centre changes and the angular velocity changes then there will be a unique point at which these two cancel, leaving no change in linear velocity.
 
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haruspex said:
If the linear velocity of the mass centre changes and the angular velocity changes then there will be a unique point at which these two cancel, leaving no change in linear velocity.
I tried to express change in angular velocity, which is
MΔv=J and Mk02 Δw = (d+1.3)J
Δv+Δw=0
so I get,
J/M + (dgrip+0.8)(d+1.3)J/ Mk02 = 0
Why can't I get the answer ?
 
Clara Chung said:
(d+1.3)J
Where does the 1.3 come from? What axis are you using here?
Clara Chung said:
Δv+Δw=0
You cannot add a velocity to an angular velocity.
You are trying to express the fact that a certain point does not change linear speed. How does its speed depend on the speed of the mass centre and its distance from the mass centre?
Be careful with signs.
 
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haruspex said:
Where does the 1.3 come from? What axis are you using here?

You cannot add a velocity to an angular velocity.
You are trying to express the fact that a certain point does not change linear speed. How does its speed depend on the speed of the mass centre and its distance from the mass centre?
Be careful with signs.
I am using the rotational pivot. Am I right?
 
Clara Chung said:
I am using the rotational pivot. Am I right?
Does that fit with the way k0 is defined?
 
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haruspex said:
Does that fit with the way k0 is defined?
Thank you so much. I solved it by using the centre of mass frame^^
 
Clara Chung said:
Thank you so much. I solved it by using the centre of mass frame^^
Very good.
For problems involving angular momentum, you should always use an axis that is either a point fixed in an inertial frame or the mass centre. Anything else can lead to a wrong result.
 

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