# Moment of Inertia

1. Nov 21, 2015

### Shawkify

1. The problem statement, all variables and given/known data
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 [Broken]

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

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

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

3. The attempt at a solution

Ui = KEf
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.

Last edited by a moderator: May 7, 2017
2. Nov 21, 2015

### haruspex

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

3. Nov 21, 2015

### Shawkify

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