Each wheel is a solid disk of mass 1.80000000000000 kg. On the horizontal surfaces the center of mass of each?

Question

Each wheel is a solid disk of mass 1.80000000000000 kg. On the horizontal surfaces the center of mass of each wheel moves with a linear speed of 6 m/s.

(b1) What is the algebraic expression for the vertical height h that the rolling wheel reaches on the incline when it comes to a momentary halt? Express your answer in terms of the potential energy Epotential, the mass m of the wheel, and the magnitude g of the acceleration due to gravity.
(b2) What is the vertical height h that the rolling wheel reaches on the incline when it comes to a momentary halt?

Answer 1

KE = mv^2/2 + Iw^2/2 (see ref.)
I (disk) = mr^2/2
w = v/r
Iw^2/2 = (mr^2/2*v^2/r^2)/2 = mv^2/4
KE = mv^2/2 + mv^2/4 = 0.75*mv^2
PE = KE
mgh = 0.75*mv^2
(ans. b1:) h=0.75v^2/g
b2. Udoit!

P.S. Question b1 is badly phrased. Expressing h in terms of PE, m and g is simply h=PE/(mg). What use is that?