# Angular Simple Harmonic Motion

1. May 13, 2015

### LucasCammarata

1. The balance spring of a watch is a hoop 1.2 cm in diameter, with a mass of 0.65 g. If the watch is running 45 seconds per day too fast, by what percentage should the rotational inertia of the hoop be changed?

2. Relevant equations: I = mR^2
Ia = -k(theta)
x(t) = Xm Cos(wt + @) (just using @ for phase constant)
T = 2pi ( I/mgL)^0.5

3. Rotational inertia = (0.00065 kg) x (0.006)^2 = 2.34 x 10^-8 I actually have no idea where to go from there.

2. May 13, 2015

### BvU

Hello LC, welcome to PF !

You don't want the value of the inertia, you only want the change ! So you could just as well call it $I_0$, from which you can calculate a $T_0$. You want a $T_1$ which is soandosmuch over soandso times $T_0$. That tells you something about $I_1$ in terms of $I_0$ !

Cryptic ? Give it a try and post.

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