A certain alarm clock ticks four times each second, with each tick representing half a period. The balance wheel consists of a thin rim with radius 0.55 cm, connected to the balance shaft by thin spokes of negligible mass. The total mass of the balance wheel is 0.90 g. (a) What is the moment of inertia of the balance wheel about its shaft? (b) What is the torsion constant of the coil spring (Fig. 14.19)?
Solution 41E The number of ticks per second tells us the time period(T) and therefore the frequency. 2 We can use the formulae I= MR (thin rim) to find the moment of inertia(I) of the balance wheel about its shaft . Then equation T=2 I allows us to calculate the torsion constant . Step 1 of 2: Ticks four times each second implies 0.25 s per tick. Each tick is half a period, so T = 0.50s and f =1/T = 1/0.5= 2 Hz 2 3 2 2 8 2 Thin rim implies I=MR =(0.90× 10 ) × (0.55 × 10 ) = 2.7× 10 kg m