Kinematics question(angular velocity)

[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?

 

[PeroK]

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?

 

[PeroK]

What is wrong with my attempt?

You've assumed that the cylinder has translational speed before it is placed on the surface.

 

[mcchoy528]

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.

 

[PeroK]

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

 

[mcchoy528]

How can I calculate the final angular velocity? Is the final angular velocity=v/r?

 

[mcchoy528]

I think I have got the correct approach.
1/2 I ω_i²=1/2mv²+1/2 I ω_f²
v=√1/3r²ω_i²