15. Rotational Equilibrium

Which method would be most helpful in locating the center of gravity of an irregularly shaped object?

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

Given a uniform semicircular plate of radius $R$, what is the distance from the flat edge to the centroid of the plate?

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

The famous Leaning Tower of Pisa doesn't topple over because its center of gravity is: $center of gravity$

The Leaning Tower of Pisa is 55 m tall and about 7.7 m in radius. The top is 4.5 m off center. Is the tower in stable equilibrium? If so, how much farther can it lean before it becomes unstable? Assume the tower is of uniform composition.

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

When Dr. Hewitt holds a broom horizontally by its handle, with the bristles on one end and the handle on the other, where is the $\mathrm{center} \mathrm{of} \mathrm{gravity}$ of the broom located?

A 50-story building is being planned. It is to be 180.0 m high with a base 46.0 m by 76.0 m. Its total mass will be about 1.8 x 10⁷ kg, and its weight therefore about 1.8 x 10⁸ N. Suppose a 200-km/h wind exerts a force of 950N/m² over the 76.0-m-wide face (Fig. 12–86). Calculate the torque about the potential pivot point, the rear edge of the building (where $\overrightarrow{F_E}$ acts in Fig. 12–86), and determine whether the building will topple. Assume the total force of the wind acts at the midpoint of the building’s face, and that the building is not anchored in bedrock. [Hint: $\overrightarrow{F_E}$ in Fig. 12–86 represents the force that the Earth would exert on the building in the case where the building would just begin to tip.]

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.) 

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

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?

Which of the following best defines the center of gravity of a body?

The center of gravity of a $\mathrm{basketball}$ is located _______.