Centrifugal Force in Angular SHM: Explained

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Discussion Overview

The discussion revolves around the role of centrifugal force in the context of angular simple harmonic motion (SHM). Participants explore whether centrifugal force should be considered in free body diagrams when analyzing the motion of a bob suspended by a string, particularly at various positions between the mean and extreme positions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether centrifugal force (mv^2/r) acts at any position during angular SHM, seeking clarification on the scenario.
  • One participant describes a scenario where the bob moves in a circular arc and suggests that centrifugal force should act outward when the bob has velocity, but notes that in the case of small angular amplitudes, the motion resembles a straight path, implying no centrifugal force.
  • Another participant emphasizes that in a general situation, the only forces acting are gravity and the tension in the string, with tension providing the necessary centripetal force and gravity acting tangentially to the motion.
  • Further discussion highlights that for larger displacements, tension increases significantly, referencing experiences of increased g-forces in fairground rides, while reiterating that the SHM approximation is valid primarily for small displacements.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of including centrifugal force in free body diagrams, with some arguing for its relevance in certain scenarios while others maintain that it is not applicable under the conditions of small angular displacements. The discussion remains unresolved regarding the general applicability of centrifugal force in this context.

Contextual Notes

The discussion highlights limitations related to the assumptions made about angular amplitude and the definitions of forces involved in the motion. The dependency on specific scenarios and the conditions under which SHM applies are also noted.

Jon Drake
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Does centrifugal force (mv^2/r) act in any position of angular SHM? Please explain.
 
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Jon Drake said:
Does centrifugal force (mv^2/r) act in any position of angular SHM? Please explain.

You might need to explain your question! Can you give a bit more detail of the scenario you are asking about?
 
Suppose that a bob is suspended by a light string, and the position of the bob is somewhere between its mean and extreme position. Then it does have a velocity and it moves in a circular arc, so (mv^2/r) should act outward. At the same time in angular SHM we take very small angular amplitude, where the object moves almost in a straight path. In that case there is no centrifugal force. So, in a general situation, should we consider the centrifugal force in the free body diagram or not?
 
Jon Drake said:
Suppose that a bob is suspended by a light string, and the position of the bob is somewhere between its mean and extreme position. Then it does have a velocity and it moves in a circular arc, so (mv^2/r) should act outward. At the same time in angular SHM we take very small angular amplitude, where the object moves almost in a straight path. In that case there is no centrifugal force. So, in a general situation, should we consider the centrifugal force in the free body diagram or not?

There are only two forces: gravity and the tension in the string. The tension cancels out the force of gravity along the line of the string and provides the centripetal force. Gravity acts tangential to the motion.
 
Jon Drake said:
So, in a general situation, should we consider the centrifugal force in the free body diagram or not?
The force of the string on the bob is centripetal and that is the tension. For a big displacement, the tension will increase noticeably. Remember the g forces on fairground rides? You are 'pulling 3g' at the bottom of a rigid swing that starts off vertical. However, the SHM approximation only applies to small displacements because it is only then that the restoring force is (near enough) proportional to the displacement (which is the definition of SHM).
 

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