# Linear speed and rotational quantity

1. Jun 30, 2008

### baylorbelle

What linear speed must a 6.0×10−2 hula hoop have if its total kinetic energy is to be 0.15 J ? Assume the hoop rolls on the ground without slipping.

So, i know that the formula for linear momentum is p=mv. however, the hoop is circular, meaning it has to have a rotational velocity (omega). I cant seem to figure out how the Joules play into any equation that helps link linear and rotational speeds. Anyone know of any formulas I can use for this problem?

2. Jun 30, 2008

### Staff: Mentor

If something is both translating and rotating, how do you determine its total kinetic energy?

What does "rolling without slipping" tell you about how translational speed relates to rotational speed?

3. Jun 30, 2008

### baylorbelle

if something is rolling without slipping, it has rotational speed but not translational speed?

4. Jun 30, 2008

### Staff: Mentor

No, that would be an example of pure rotation. (And complete slipping!)

Read this: Kinetic Energy of Rolling Object

Last edited: Jun 30, 2008