Assignment:
Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material.
1) By what factor would the frequency change?
2) Would the frequency increase or decrease by the factor found in part (a)? increase or decrease?
3) By what factor would the torsion constant need to be changed to make the smaller balance wheel oscillate at the original frequency?
4) Would the torsion constant need to be increased or decreased by the factor found in part (c)? increased or decreased?