# Uncertainty Question

1. Jul 8, 2010

### Ush

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

this isn't really a word problem, it's part of a series of calculations from a physics lab
in this lab,
Ug = energy at initial position
Ug -> Ekrot + Ek at final position

I need to calculate
1. Ekrot
2. Moment of Inertia
3. angular velocity

2. Relevant equations

Ug = mgh
Ekrot = ½Iѡ²
Ek = ½mv²

ѡ = v/r

v = 2h/t (in this case)

m = 0.100m ± 0.0005
g = 9.8m/s²
h = 0.800m ± 0.0005
v = 0.21m/s ±0.01
r = 0.004m ± 0.002
t = 7.66s ± 0.08

3. The attempt at a solution

mgh = Ekrot + ½mv²
Ekrot = mgh - ½mv²

Δmgh = |dy/dm mgh| + |dy/dh mgh|
= |dy/dm gh| + |dy/dh mg|
= |dy = ghΔm| + |dy = mgΔh|

relative error = Δmgh / mgh

= |ghΔm / mgh| + |mgΔh / mgh|
= |Δm/m| + |Δm/h|

similarly, the relative uncertainty of ½mv² is..

Δ½mv²/½mv² = |Δm/m| + |2Δv/v|

so.... now what?
We're not allowed to add relative uncertainties, i really don't know what to do here
We can add absolute uncertainty but I have no knowledge on how to calculate absolute uncertainty.

also, the angular velocity, ѡ, = v/r. There is an uncertainty on v and an uncertainty on r. so how do I calculate moment of inertia (I) after I have the uncertainty of Ekrot?? The uncertainties of ѡ and r weren't used when when calculating uncertainty of Ekrot (unless my steps above are way off.. which i doubt)

I'm very confused, any help would be appreciated
thank you
~Ush

Last edited: Jul 8, 2010
2. Jul 8, 2010

### Tusike

As far as I know, relative uncertainties can't be added. I normally calculate using absolute ones, in a way so that I calculate the min and max values, and use the average.

For example, say t = 10+-0.1 secs and s = 50+-1meters, simple linear motion.

v(min) = 49m / 10.1 secs = 4.85
v(max) = 51m / 9.9secs = 5.15

So then I would say that v = 5m/s +- 0.15m/s.
Then follow the same routine to calculate other things, perhaps I=mv, according to this.

3. Jul 8, 2010

### Ush

1) You cannot calculate max / min in this because some of the measurements were taken only once and some were taken as an average.
2) moment of inertia ≠ inertia

4. Jul 8, 2010