# 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:

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 Helper
Gold Member
2020 Award

## 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:

v=rω

## The Attempt at a Solution

v=0.1 (5*2π)=π m/s

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

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
Homework Helper
Gold Member
2020 Award
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
Homework Helper
Gold Member
2020 Award
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?

Last edited by a moderator:
mcchoy528
I think I have got the correct approach.
1/2 I ωi2=1/2mv2+1/2 I ωf2
v=√1/3r2ωi2

PeroK