# Kinematics question(angular velocity)

1. Dec 6, 2017

### mcchoy528

1. The problem statement, all variables and given/known data
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:

2. Relevant equations
v=rω

3. The attempt at a solution
v=0.1 (5*2π)=π m/s

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

2. Dec 6, 2017

### PeroK

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?

3. Dec 6, 2017

### PeroK

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

4. Dec 6, 2017

### 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.

5. Dec 6, 2017

### PeroK

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

6. Dec 6, 2017

### mcchoy528

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

Last edited: Dec 6, 2017
7. Dec 6, 2017

### mcchoy528

I think I have got the correct approach.
1/2 I ωi2=1/2mv2+1/2 I ωf2
v=√1/3r2ωi2