- #1
Physics Dad
- 55
- 1
Homework Statement
Hi,
I recently performed a lab experiment for calculating the moment of inertia and spring constant of a couple of equal masses on a steel rod. I had to do this experiment at the exact same time as performing another experiment so I was unable to perform any calculations in the lab, just simply gather data.
The first part of the experiment requires the calculation of the torsional spring constant (k) using a plot of T2 v r2 and as I was unable to perform calculations in the lab, I was hoping someone could provide a little guidance here.
Homework Equations
T2=4π2(I/k)
r2=I/2m
y=Δx+c (where Δis the gradient (wrong symbol, I know))
(T is the period of one single oscillation, r is the radius of the masses from the centre of mass)
The Attempt at a Solution
I know that T2 = 4π2(I/k) and that r2 = I/2m (because there were two equally spaced masses on a thin rod of negligible mass). If I then plot T2 v r2 in JLineFit and equate this to the the equation of a straight line, I should find that T2 = Δr2+c.
Subbing in my values for T2 and r2 and solving for k, I get the equation to be:
4π2(I/k) = (ΔI/2m)+c
so if I start by multiplying through by k I get
4π2I=k((ΔI/2m)+c)
so
4π2I/((ΔI/2m)+c)=k
so
k = 4π2/((Δ/2m)+c)
All I really want to know is if my rearranging is correct (do the I's cancel?). I get very confused here!
Thanks
Last edited: