The pendulum in the figure consists of a uniform disk with radius r = 18.0 cm an
ID: 2252500 • Letter: T
Question
The pendulum in the figure consists of a uniform disk with radius r = 18.0 cm and mass 810 g attached to a uniform rod with length L = 690 mm and mass 300 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation.
The pendulum in the figure consists of a uniform disk with radius r = 18.0 cm and mass 810 g attached to a uniform rod with length L = 690 mm and mass 300 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation.Explanation / Answer
a) I_D = 0.5 Mr^2 + M(L+r^2) = 598.26
I_R = mL^2/12 +m(L/2)^2 = mL^2/3 = 47.61
I_P = 598.26 + 47.61 = 0.646 kg m^2
b) Id = L+r = 0.69+0.18 = 0.87 m
Ir = L/2 = 0.345 m
Ip = 810*0.87+300*0.345 / 810+300 = 0.731 m
c) T = 2*3.1415sqrt(0.646/810+310)*9.8*0.731 = 0.056 s
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