Advanced Concepts in Moment and Center of Mass Quiz

What is the most accurate definition of the center of mass of an object?

• The point where the weight of the object is concentrated
• The average position of all mass in an object
• The geometric center of the object
• The point where the object can pivot

For a uniform rod of length L pivoted at one end, where is the center of mass located?

• At the pivot point
• At L/2 from the pivot
• At L/4 from the pivot
• At the opposite end of the rod

How is the center of mass calculated in a system of particles?

• By averaging the positions of the particles
• By summing the products of mass and position of each particle and dividing by the total mass
• By finding the midpoint of the system
• By using the maximum distance between any two particles

What happens to the center of mass of a system when one of the particles is removed?

• It remains unchanged
• It moves towards the remaining particles
• It moves away from the remaining particles
• It becomes undefined

Which scenario would result in a change in the center of mass of a system?

• Adding a mass at the center of mass
• Distributing mass evenly across the object
• Removing a mass from one side of the object
• Rotating the object around its center of mass

Where is the center of mass located if two equal masses are placed at opposite ends of a line segment?

• At one of the masses
• At the midpoint of the line segment
• Outside the segment
• At the average of the two positions

In a uniform gravitational field, how does the center of mass affect the stability of an object?

• A higher center of mass increases stability
• A lower center of mass increases stability
• The center of mass has no effect on stability
• Stability is only affected by the weight of the object

What is the relationship between torque and moment?

• Torque is the vector quantity related to moment
• Moment is the scalar quantity related to torque
• Torque and moment are the same concepts
• Moment is the product of torque and distance

If a rigid body rotates about its center of mass, how does this affect the motion of the body?

• It will not rotate at all
• It will rotate with constant angular velocity
• It will experience translational motion
• It will rotate and translate simultaneously

Which method can be used to find the center of mass of a composite object?

• The Pythagorean theorem
• The principle of moments
• The method of sections
• The weighted average of the centers of mass of the individual components