Problem Graphic

Justin Time Clocks Inc. manufactures grandfather clocks with swinging pendulums. To make clocks that keep accurate time, the engineers must determine the mass moment of inertia of the pendulum.

What is known:

• The pendulum pivots about the top at O.
• The pendulum consists of a slender rod with a disk attached to the end.
• The rod has a length L_r = 1.2 ft, a mass m_r = 0.5 slugs, and its cross section is circular with a radius r_r = 0.05 ft.
• The disk has a thickness t_d = 0.1 ft, a radius r_d = 0.4 ft, and mass m_d = 2.67 slugs.
• The rod and disk are made from a homogeneous material with density r.

Problem Dimensions

What is the moment of inertia of the pendulum about an axis L_o passing through its pivot point 0 at the top of the rod?

• Determine the moment of inertia of each part about an axis passing through each part's center of mass.
• Determine the moment of inertia of each part about an axis passing through O.
• Combine the moment of inertia of each part to determine the total moment of inertia of the pendulum about an axis passing through the point O.