Calculating Rotational & Transitional KE of Rolling Cylinder

[smilingsteph]

My textbook is not helping me on this, so I'd love some help.

A cylinder is rolling down a ramp, without slipping. I have the total kinetic energy, but now need to know the rotational kinetic energy and transitional kinetic energy at the bottom of the ramp.

I have the mass, radius, length, w, v, and I of the cylinder and the height and length of the ramp. I know it should be super easy at this point, as I know the total energy. But nothing's working. HELP! I have that: KE tot = 1/2 I x w^2 + 1/2 m x v^2. Any guidance?

 

[Hootenanny]

My textbook is not helping me on this, so I'd love some help.

A cylinder is rolling down a ramp, without slipping. I have the total kinetic energy, but now need to know the rotational kinetic energy and transitional kinetic energy at the bottom of the ramp.

I have the mass, radius, length, w, v, and I of the cylinder and the height and length of the ramp. I know it should be super easy at this point, as I know the total energy. But nothing's working. HELP! I have that: KE tot = 1/2 I x w^2 + 1/2 m x v^2. Any guidance?

Since the cylinder is rolling without slipping, can you relate the angular velocity to the linear velocity?

 

[smilingsteph]

yes i would assume so. v=vo + at to w=wo + alphaT

 

[Hootenanny]

yes i would assume so. v=vo + at to w=wo + alphaT

They weren't the equations I was thinking of, there is one equation which directly relates the angular velocity of a cylinder to the linear velocity of the surface of the cylinder.

 

[smilingsteph]

Ohhh really? I was looking online for that and haven't had any luck so far. I'll continue to look! Thanks!

 

[Hootenanny]

Ohhh really? I was looking online for that and haven't had any luck so far. I'll continue to look! Thanks!

Perhaps:

$$\omega =\frac{v}{r}$$

would help.

 

[smilingsteph]

ohhh ok thanks! i'll see if that works. THANKS!