Calculating Moment of Inertia Homework: Soccer Ball

[Shawkify]

Homework Statement

An object rolls down a ramp starting from rest, demonstrate symbolically the calculation needed to go from time given to a measured κ value here. Pick your favourite object and perform the calculation.
d, m, R, t, h are known
http://puu.sh/luare/10352d0479.png

Soccer Ball:
m = 331.2 kg
R = 10.54 cm
t = 2.25 s
d = 0.2805 m
h = 0.0445 m

Homework Equations

Derived from an earlier problem:
a = (g*h)/(d*(1+k))
d = 1/2*a*Δt²

KE_total = 1/2*m*v² + 1/2*I*ω²
I = κ*m*R²
U = m*g*h
v = v₀ + a*t

The Attempt at a Solution

U_i = KE_f
m*g*h = 1/2*m*v² + 1/2*I*ω²
m*g*h = 1/2*m*v² + 1/2*κ*m*R²*(v/R)²
g*h = 1/2*v² + 1/2*κ*v²
κ = (g*h)/v² - 1
v = (g*h)/(d*(1+k))*t

Solving a system of equations gives me:
v = (2*d)/t
κ = (g*h*t² - 2*d²)/(2*d²)

Plugging in values gives me v = 1.65 m/s and k = 30.8. Compared to a chart which gives a value of κ = 2/3 for a thin spherical shell, my κ value is extremely large.

 

[haruspex]

g*h = 1/2*v² + 1/2*κ*v²
κ = (g*h)/v² - 1

You lost a factor of 2 there, but it reappeared later.

t = 2.25 s

That seems like a very long time, given the set-up. It should be more like 0.6 s.

v = (2*d)/t
gives me v = 1.65 m/s

How do you get that from these numbers? (2*0.2805)/2.25=0.25

 

[Shawkify]

You lost a factor of 2 there, but it reappeared later.

That seems like a very long time, given the set-up. It should be more like 0.6 s.

How do you get that from these numbers? (2*0.2805)/2.25=0.25

Thanks for your help, I've been told the units for this problem were all messed up and have successfully solved the corrected version.