Conceptual Dynamics - Independent Learning

Center of Mass / Gravity

How do the concepts of center of mass and center of gravity differ? When do they coincide?

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The center of mass is the mean location of all the mass in a given body or system.
The center of gravity is the mean location of all the mass in a given body or system.
The center of mass is the mean location of the gravitational force acting on the body.
The center of gravity is the mean location of the gravitational force acting on the body.
The center of mass and center of gravity always coincide when the body has uniform density.
The center of mass and center of gravity always coincide when the body is located in a uniform gravitational field.

Why do we need to know where the center of gravity of a body is located?

How do the concepts of centroid (center of volume) and center of mass differ? When do they coincide?

Check all that apply.

The center of mass is the mean location of all the mass in a given body or system.
The centroid is the mean location of all the mass in a given body or system.
The centroid of a body is the center of its volume.
The center of mass and centroid always coincide when the body has uniform density.
The center of mass and centroid always coincide when the body is located in a uniform gravitational field.

Center of mass for a system of particles

Consider the system of particles shown. The location of the overall center of mass (r_G) is equal to the weighted average of the locations of each individual particle's center of mass.

r_G = ∑m_ir_i/m

Center of mass for a rigid body

A rigid body is a collection of infinitesimally small particles as shown in the figure. Therefore, the location of the center of mass of a rigid body is calculated using the integral form of the system of particles equation above.

r_G = (1/m)∫r dm

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