What type of problem is this? Physics 1 practice final.

[chloeishere]

Hi all! Just registered for this forum, wish I had gone looking for help earlier this semester, this would have been nice.
My physics final is tomorrow, and I've been trying to finish up the practice final (I have my calculus 3 final and several other assignments also due tomorrow), but I can't figure out what I should be doing for this question. Is it a rotational problem? Simple kinematic? Any hints?
Here it is:
A solid spherical ball with an uniform density and 5 cm in radius has an initial velocity of 2 m/s. It rolls up a plane inclined at 30 degrees, where it briefly comes to rest before rolling back down. What distance d does the ball roll up the incline?
The way it was phrased initially made me think of the moment of inertia, since he mentioned the ball had uniform density, which means row (I think that's how it's spelled, the curly greek "p" ) is constant, and I equals 2/5 MR^2 (but we don't know M!) I can't figure out what equation to use! Then I thought maybe I was being too complicated, and I looked at the kinematic equations, but I don't think that'll work either-- I don't know delta t or anything.
I've spent about an hour flipping through my notes and the textbook, and I still don't know what to do! Time is of the essence right now, so I don't have any more time to waste staring blankly at this question. I'm not a natural talent with physics, unfortunately.
Thanks so much!

 

[BobG]

Work-Energy Thereom.
$$0=mgh_f - mgh_i + \frac{1}{2}mv^2_f - \frac{1}{2}mv^2_i + \frac{1}{2}I\omega^2_f - \frac{1}{2}I\omega^2_i$$
Half the terms go to zero, so it's not as imposing as it might look at first glance.

 

[Astronuc]

Density is often given the Greek letter, rho, $\rho$.

However, looking at the equation that BobG provided, the mass m is found in all terms, so dividing the equation by m eliminates it as a variable.

Also - one might find this useful - http://hyperphysics.phy-astr.gsu.edu/hbase/mi
and - http://hyperphysics.phy-astr.gsu.edu/hbase/inecon.html

 

[chloeishere]

Thanks!

Yeah, that looks like the right equation for me! Though at first I wasn't sure about the mass, but the moment of inertia term does contain mass, duh. Thanks for all the help-- I'm sure I'll be able to get it now!

On a related note, so that's how you spell rho... that makes much more sense then a spelling that reminded me of "row, row, row your boat"...