Advanced Rotational Velocity Question

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Homework Help Overview

The problem involves a particle of mass m rotating with uniform speed on the inside of a parabolic frictionless bowl, specifically in a horizontal circle with a radius of 0.4 meters. The surface of the bowl makes an angle of 20 degrees with the vertical at the position of the particle, and the discussion centers around determining the angular velocity of the particle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to approach the problem, with one noting the need to analyze forces acting on the particle, including weight and normal reaction force. Questions arise regarding the expression for the normal reaction force and its relationship to the forces acting on the particle.

Discussion Status

The discussion is ongoing, with participants exploring the relationships between the forces involved. Some guidance has been offered regarding the drawing of force diagrams and the need to analyze the resultant forces to understand the dynamics of the situation. Multiple interpretations of the normal reaction force are being considered.

Contextual Notes

Participants are grappling with the implications of the particle's motion in a circular path and the effects of the angle of the surface. There is a lack of consensus on the correct expression for the normal reaction force, indicating a need for further clarification and exploration of the problem's assumptions.

Victorzaroni
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Homework Statement



A particle of mass m rotates with a uniform speed on the inside of a bowl's parabolic frictionless surface in a horizontal circle of radius R=0.4 meters as shown below. At the position of the particle the surface makes an angle θ=20 degrees with the vertical. The angular velocity of the particle would be:

Homework Equations



?

The Attempt at a Solution



I have no idea what to do. The answer is 8.2rad/s
 

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Victorzaroni said:

Homework Statement



A particle of mass m rotates with a uniform speed on the inside of a bowl's parabolic frictionless surface in a horizontal circle of radius R=0.4 meters as shown below. At the position of the particle the surface makes an angle θ=20 degrees with the vertical. The angular velocity of the particle would be:

Homework Equations



?

The Attempt at a Solution



I have no idea what to do. The answer is 8.2rad/s

The object is traveling in a circle, so the net force is is horizontal towards the centre.
The acting forces - which combine to make that net force - are weight (vertically down) and the Normal Reaction force which acts at right angles to the slope, so is in a direction 20o above the horizontal.

Draw that triangle of forces (as arrows as usual) and you will be able to use trig and/or Pythagoras to calculate the size of the centripetal acceleration.

From that you can get the angular velocity.
 
how would I express the normal reaction force? I've got Fc=Fnet, so mac=mg+N. What is N? Is it mgsinø, mgcosø? What is it?
 
Victorzaroni said:
how would I express the normal reaction force? I've got Fc=Fnet, so mac=mg+N. What is N? Is it mgsinθ, mgcosθ? What is it?

I am not sure it is either. If the mass was sitting on a slope of that angle it would be one of them - but this mass is circulating, so the reaction force has to be much larger.

The weight force would be represented by an arrow, vertically down.
To add the Reaction Force, you draw its arrow starting at the end of the weight force arrow [join the arrows head to tail]
The Reaction arrow is angled up at 20 degrees.
It has to be long enough to make the resultant force horizontal.

Try drawing it - then analysing the resulting picture.
 

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