15. Rotational Equilibrium

A 70 kg, 1.90 m man doing push-ups holds himself in place making 20° with the floor. His feet and arms are, respectively, 1.15 m below and 0.4 m above his center of mass. You may model him as a thin, long board, and assume his arms and feet are perpendicular to the floor. How much force does the floor apply to each of his hands? (Use g=10 m/s².) 

A uniform rod is 2.00 m long and has mass 1.80 kg. A 2.40 kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite object to be 1.20 m from the left-hand end of the rod?

The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods. Find the coordinates of the center of mass.

The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. Find the coordinates of the center of mass.

Two balls are connected by a 150-cm-long massless rod. The center of mass is 35 cm from a 75 g ball on one end. What is the mass attached to the other end?

In the context of vehicle dynamics, what is the point where the mass of the vehicle is considered to be concentrated and balanced?

In the Earth-Moon system, where is the center of mass ($\mathrm{barycenter}$) located relative to the two bodies?

The center of mass of two objects orbiting each other is always which of the following?