Characteristics of a rigid body.

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Homework Help Overview

The discussion revolves around the characteristics of a rigid body, specifically focusing on the concepts of angular velocity and angular acceleration as they relate to points within the body. Participants explore the implications of differing velocities on the definition of a rigid body.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question why angular velocity and acceleration are the same for all points on a rigid body. Some explore hypothetical scenarios, such as differing velocities at the front and back of a car, to illustrate potential contradictions to the rigid body definition. Others attempt to deduce relationships between angular velocities through geometric reasoning involving fixed angles and points.

Discussion Status

The discussion is active, with participants providing hints and exploring various interpretations of the rigid body concept. Some guidance has been offered regarding the definition of 'rigid', and there is an ongoing examination of the implications of angular velocities being equal across points.

Contextual Notes

Participants are considering the implications of the rigid body definition and the constraints that arise when points within the body exhibit different velocities. The discussion reflects a mix of theoretical exploration and practical implications of the rigid body model.

andyrk
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Why is the angular velocity and angular acceleration(if the rigid body has some) same for all points on a rigid body?
 
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What would happen if the front and back of a car had different velocity?
 
Take an angle fixed by three points A, B, C within the body. As the body rotates, the angle ABC must be preserved. So AB and BC must rotate by the same angle. Differentiating, deduce that the angular velocities and accelerations must also be the same.
 
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haruspex said:
Take an angle fixed by three points A, B, C within the body. As the body rotates, the angle ABC must be preserved. So AB and BC must rotate by the same angle. Differentiating, deduce that the angular velocities and accelerations must also be the same.

But this gets that angular velocity of AB=angular velocity of BC
How does this get that angular velocity of A,B,C are equal?
 
Hint: look up the definition of 'rigid'.
 
The points are arbitrary. So the centre of rotation can be B. That means the angular velocity of A is the same as the angular velocity of AB...

Angular velocity of A = Angular velocity of AB = Angular velocity of CB = Angular velocity of C

It's why I asked the question above. If two points on a body have different velocity (angular or linear) then those points must get closer together or further apart which would imply it's not a rigid body.
 

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