Spiral balance spring questions

[mguysmith]

1.
First off i am not a student per say, this is related to my hobby
I am repairing an old clock and need to replace the balance spring which is completely missing. I have located ONE source that may carry suitable springs but I cannot figure out which spring to order.

The spring supplier sorts their springs by strength as expressed in the following units
gram/cm/100 degrees.

Given that my balance wheel is
14mm in diameter
has a mass of 0.8 grams
osscilates through an arc og 270 degrees in each direction
and osscilates 4 times per second
mb it down
how do i determine the correct size balance spring?

please be advised that i am an english major and have no physics background at all, so don't be afraid to du

Homework Equations

The Attempt at a Solution

 

[jbsteele]

To determine the correct size balance spring for your clock, you will need to calculate the torque that the spring must provide in order to move the balance wheel. This torque can be calculated using the equation Torque=Mass x Angular Velocity x Radius. To do this, you must first convert the angular velocity from revolutions per second (4 rev/s) to degrees per second (2160°/s). Next, you need to calculate the torque the spring needs to provide. This is equal to the product of the mass (0.8 g), the angular velocity (2160°/s), and the radius of the balance wheel (7mm). So the torque required is 0.8 g * 2160°/s * 7mm = 8928 g-mm/s. Finally, you need to convert this torque value into the units that the spring supplier uses: gram/cm/100 degrees. To do this, divide the torque value (8928 g-mm/s) by 100 degrees and multiply it by the radius of the balance wheel (7mm) to get the result in grams/cm. This gives us a result of 126.97 g/cm. Therefore, you should order a balance spring with a strength of 126.97 g/cm from the supplier.