The pendulum in the figure consists of a uniform disk with radius r = 18.0 cm an

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 of the disk: ID=0.5Mr^2+M(L+r)^2 = 0.626

I of the rod: IR=mL^2/12 + m(L/2)^2= mL^2/3 = 0.048

I of the pendulum: IP= ID+ IR =0.674 kgm2

b

COM of the disk: lD=(L+r) =0.87 m

COM of the rod: lR=L/2 = 0.345m

COM of the pendulum: lP= (MlD+ mlR)/(M+m)= 0.728m

c

h=0.728m

I = 0.674 kgm2

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