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**[SOLVED] Rotational Momentum**

This is my first attempt at asking a question on here so please be gentle. I've been working on this problem for almost an hour and a half

## Homework Statement

In a circus performance, a large 3.0 kg hoop with a radius of 1.6 m rolls without slipping. If the hoop is given an angular speed of 5.6 rad/s while rolling on the horizontal and is allowed to roll up a ramp inclined at 18° with the horizontal, how far (measured along the incline) does the hoop roll?

**2. Relavent Equations**

1/2Iα^2=Rotational Momentum

1/2mv^2=kintetic Momentum

mgh=potential Momentum

V(tangent)=rω

I=1/2mr^2

**3. Attempt a Solution**

First i tried getting the rotational momentum and when i put the numbers in it comes out to about 60.221 kgm/s and then i set it equal to the potential momentum equation and got the height is 2.048m. However this answer came out as wrong.

So then i tried getting the tangential velocity and got 8.960 m/s and put that into the kentetic momentum equation and got 120.422 kgm/s (double what i got for rotational momentum) and set that to the potential energy equation and got 4.096m. Which is also wrong.

I think im missing something to do with the ramp being 18 degrees above the horizontal but im not sure where to add that into my math.

Please any help would be appreciated thank you.

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