Am I doing this right? - rotational motion

[hoseA]

Hint: Consider the wheel's energy.
Consider a wheel of radius 1.23 m, mass
7.7 kg and moment of inertia I =1/2 MR^2
(it's a solid disk). The wheel rolls without
slipping in a straight line in an uphill direction 30 degrees above the horizontal. The wheel starts at angular speed 16.1 rad/s but the ro-
tation slows down as the wheel rolls uphill,
and eventually the wheel comes to a stop and
rolls back downhill.
The acceleration of gravity is 9.8 m/s^2
How far does the wheel roll in the uphill
direction before it stops? Answer in units of
m.

This is what I plan to do:

1. Use:

1/2 Iw^2 +1/2 mv^2 = mgh

by substituting Rw for v and solving for h.

2. "h" would equal the "y" component so I would then go on to use trig. to find the hypontenuse.

Would that work?

 

[andrewchang]

yes, it is correct

 

[hoseA]

Thanks for the confirmation. I don't think I'm good at canceling variables out as I got the wrong answer the first time (tried to cancel out the masses). But the second time around I just plugged in everything and it came out to a different and correct answer. :)