Kinematics question(angular velocity)

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Homework Help Overview

The discussion revolves around a problem in kinematics involving a circular cylinder that is initially rotating and then placed on a flat surface. Participants are exploring the relationship between angular velocity and translational speed, particularly in the context of rolling without slipping.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to calculate the translational speed using the formula v=rω, but there is confusion regarding the assumptions made about the cylinder's motion before and after it is placed on the surface.
  • Some participants question whether energy loss occurs when transitioning from spinning to rolling without slipping.
  • There are discussions about the conservation of rotational kinetic energy and how it relates to the final translational speed.
  • One participant raises a question about calculating the final angular velocity and its relationship to translational speed.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants have offered insights into the assumptions regarding energy conservation and the relationship between rotational and translational motion. There is no explicit consensus yet, but participants are engaging with the problem and providing guidance to each other.

Contextual Notes

Participants are navigating the complexities of the problem, including the implications of rolling without slipping and the potential energy losses that may occur. The original poster's confusion about the correct approach indicates that there may be missing information or unclear assumptions in the problem statement.

mcchoy528

Homework Statement


Question: A circular cylinder with mass of 1 kg and radius a=0.1 m is rotating about its cylindrical axis at a rate of 5 revolutions per second. It is then placed on a flat surface. Assuming that there is no dissipation at contact and the cylinder is rolling without slipping (with negligible rolling friction) on the flat surface, its translational speed is:

Homework Equations


v=rω

The Attempt at a Solution


v=0.1 (5*2π)=π m/s

The answer is 1.81m/s. Can anyone help?
 
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mcchoy528 said:

Homework Statement


Question: A circular cylinder with mass of 1 kg and radius a=0.1 m is rotating about its cylindrical axis at a rate of 5 revolutions per second. It is then placed on a flat surface. Assuming that there is no dissipation at contact and the cylinder is rolling without slipping (with negligible rolling friction) on the flat surface, its translational speed is:

Homework Equations


v=rω

The Attempt at a Solution


v=0.1 (5*2π)=π m/s

The answer is 1.81m/s. Can anyone help?

You've answered a different question. The question you have answered was:

If a cylinder is rolling without slipping at 5 rev/s then what is its translational speed.

That said, I'm not sure what the question is asking. If you put the spinning cylinder on a surface, then there must be energy loss before it gets to a state of rolling without slipping. But, the question seems to ask you to ignore this energy loss. Perhaps try that?
 
mcchoy528 said:
What is wrong with my attempt?

You've assumed that the cylinder has translational speed before it is placed on the surface.
 
how can I answer this question? The rotational kinetic energy is conserved.
1/2mv2=1/2Iω2
If I put the data into this equation, v=2.22m/s . I still can't get the answer.
 
mcchoy528 said:
how can I answer this question? The rotational kinetic energy is conserved.
1/2mv2=1/2Iω2
If I put the data into this equation, v=2.22m/s . I still can't get the answer.

Now you have assumed that the cylinder has stopped rotating and has only translational motion. Note that:

Initially the cylinder is rotating

Finally it is rolling without slipping
 
How can I calculate the final angular velocity? Is the final angular velocity=v/r?
 
Last edited by a moderator:
I think I have got the correct approach.
1/2 I ωi2=1/2mv2+1/2 I ωf2
v=√1/3r2ωi2
 
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