A Mass on a Turntable: Conceptual

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SUMMARY

The discussion centers on the motion of a small metal cylinder on a rotating turntable, specifically when the cylinder is moved from a radius R to R/2. The key conclusions are that the speed of the cylinder decreases as it moves closer to the center, as described by the equation v = Rω, where ω is the constant rate of rotation. The participants clarify that while the radius decreases, the speed actually reduces, contradicting the initial assumption that speed would increase. Additionally, the magnitude of acceleration increases due to the change in radius.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with angular velocity (ω) and linear speed (v)
  • Knowledge of the relationship between radius and speed in rotational systems
  • Basic grasp of angular momentum concepts
NEXT STEPS
  • Study the equations of motion in circular dynamics
  • Learn about the effects of radius on speed and acceleration in rotating systems
  • Explore angular momentum and its conservation in rotational motion
  • Investigate real-world applications of rotational dynamics in engineering
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Physics students, educators, and anyone interested in understanding the principles of rotational motion and dynamics in mechanical systems.

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Homework Statement


A small metal cylinder rests on a circular turntable that is rotating at a constant rate. Let R be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location R/2 from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location?

A The speed of the cylinder has decreased.
B The speed of the cylinder has increased.
C The magnitude of the acceleration of the cylinder has decreased.
D The magnitude of the acceleration of the cylinder has increased.
E The speed and the acceleration of the cylinder have not changed.

There could be more than one answers.

Homework Equations



v^2/R=magnitude

The Attempt at a Solution



So I tried out this experiment. It moves at a constant motion around the center of the mass and the speed is constant. Since it says "R/2" I decresaed the radius and the speed increases. So I think B is one of the answers. What else should I be aware of?
 
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I don't see why the speed would increase... if [tex]\omega[/tex] the rate of rotation of the turntable is the same... then the speed of the cylinder is [tex]R\omega[/tex] where R is the radius... so a smaller radius implies smaller speed... unless I'm missing something...

I'm thinking the cylinder won't rotate about its own axis if it's placed initially at rest on the turntable... because the rotation of the turntable only imparts angular momentum about the vertical axis... the axis of the cylinder is perpendicular to the vertical axis...
 
learningphysics said:
I don't see why the speed would increase... if [tex]\omega[/tex] the rate of rotation of the turntable is the same... then the speed of the cylinder is [tex]R\omega[/tex] where R is the radius... so a smaller radius implies smaller speed... unless I'm missing something...

I'm thinking the cylinder won't rotate about its own axis if it's placed initially at rest on the turntable... because the rotation of the turntable only imparts angular momentum about the vertical axis... the axis of the cylinder is perpendicular to the vertical axis...

Oh, i see. I misinterpretted the problem. Thanks for the reply.
 

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