6.1.2 The Center of Mass of a Rigid Body

Question 1

The Center of Mass of a Rigid Body

Answer 1

• When an object hangs freely from a point, its center of mass lies directly below that point. You can use this fact to physically find the center of mass of a rigid body.
• The center of mass of a continuous mass distribution:

Question 2

Which of the following facts is used to physically find a rigid body’s center of mass?

Answer 2

When an object hangs freely from a point, its center of mass lies directly below that point.

Question 3

Find the center of mass of the following triangle. Assume the triangle has a constant density of 1.

Answer 3

(4a/3, a/3)

Question 4

Find the center of mass of the following triangle. Assume the triangle has a constant density of 1.

Answer 4

(2a/3, a/3)

Question 5

A lamina is shaped like the first-quadrant quarter-circle of radius 1 shown below. Find its center of mass. Assume it has a constant density of 1.

Answer 5

(4/3pi, 4/3pi)

Question 6

Find the center of mass of the following rigid body. Assume it has constant density of 1.

Answer 6

(0, 0)

Question 7

Which of the following statements about a rigid body is true?

Answer 7

A rigid body behaves as if its mass were concentrated at the center of mass.

Question 8

Which of the following is a rigid body?

Answer 8

An iron ball.

Question 9

Which of the following is the center of mass of the semicircular disk of radius a shown below? Assume it has a constant density of 1.

Answer 9

(0, 4a/3pi)