Question

A clock balance wheel (Fig. P15.39) has a period of oscillation of 0.350 s. The wheel is constructed so that its mass of 30.0 g is concentrated around a rim of radius 0.400 cm. Figure P15.39 (a) What is the wheels moment of inertia? kg.m2 (b) What is the torsion constant of the attached spring? N m/rad

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Answer #1

Mass (M)= 30 g=0.03 kg, Radius(R)= 0.4 cm = 0.004 m. Total mass is concentrated on the rim so it is like a ring.
a) Moment of intertia(I) = MR^2

I= 0.03*.004^2 = 4.8*10-7 kg.m^2

B) Let torsional constant is K.
so, Time period (T) = 2pi*(I/K)0.5

0.35= 2*3.14*(4.8*10-7/K)0.5

K = 1.547*10-4 Nm/rad

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