Falling and sliding stick (David Morin)

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Homework Help Overview

The discussion revolves around the dynamics of a falling and sliding stick, particularly focusing on the forces acting on the stick and the motion of its center of mass (CoM). Participants are exploring concepts related to translational and rotational motion, as well as the role of normal force (N) in the context of the stick's pivot on a frictionless rail.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the inclusion of the normal force (N) in the equations of motion, with some suggesting it only serves to maintain the pivot's position. Others are exploring the implications of translational versus rotational motion, particularly whether the stick experiences vertical motion or remains in a state of equilibrium.

Discussion Status

The discussion is active, with various interpretations being explored regarding the motion of the stick and the forces acting on it. Some participants have offered insights into the necessity of considering both translational and rotational dynamics, while others are questioning the assumptions made about the pivot and the nature of the forces involved.

Contextual Notes

Participants are navigating the complexities of analyzing motion in a non-inertial frame and the implications of fictitious forces. There is a recognition that the pivot's acceleration affects the analysis, and some participants are considering the moment of inertia in relation to the stick's rotation.

  • #31
Father_Ing said:
I am a bit confused..
If we see the the rod as a rigid body that is formed by many particles, N is exerted only to the particle at the end of the rod.In my opinion, N only affects the acceleration of the particle this point (the pivot, or we can also say, the end of the rod). However,in the equation ##N -mg = ma## , I can conclude that N affects the acceleration of the whole particles.

How can N affects the whole particles' acceleration?
If you lift a suitcase up by the handle, then the handle doesn't necessarily break off from the rest of the suitcase. And, if you hold a tennis racket by the handle, then the racket head (the bit with the strings) moves as well when you swing the handle.

Have you made any progress at solving this problem?
 
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  • #32
PeroK said:
Have you made any progress at solving this problem?
Yep! I have made it through the 2nd question. I still have some problems regarding the concepts, though.
haruspex said:
Because the rod is rigid, so each particle transfers force and torque to the next.
So, each particle has a force ##dN## exerted on it, and the value of ##dN## differs from each particle?
 
  • #33
Father_Ing said:
So, each particle has a force ##dN## exerted on it, and the value of ##dN## differs from each particle?
Yes, each particle on the rod must be subject to the force required by the constraint that the rod remains rigid. ##N## is an external force applied at the pivot. ##dN## doesn't make sense in this context.

There will be a distribution of internal forces along the rod. If you have calculated the motion of the rod, you may calculate the motion of every point on the rod and hence the force on that point.

The point is that the internal forces cancel (Newton's third law) and the external forces determine the motion. Unless the rod breaks, the internal forces are irrelevant.
 
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  • #34
Alright! Thanks.
 

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