55 Questions
What is the equation for the x-coordinate of the center of mass of n particles in three dimensions?
x_{CM} = \frac{\sum_{i=1}^{n} m_i x_i}{\sum_{i=1}^{n} m_i}
What is the center of mass?
The center of mass is a special point that describes the overall motion of a system.
Does the translational motion of the center of mass depend on other motions like rotation or vibration?
No, the translational motion of the center of mass is independent of other motions like rotation or vibration.
How can the center of mass of a system be described?
The center of mass of a system can be described as the average position of the system's mass.
Where is the center of mass located in a system consisting of two particles connected by a rigid rod?
The center of mass is located somewhere on the line joining the two particles and is closer to the particle with the larger mass.
What happens when a force is applied above the center of mass in a system?
The system rotates clockwise.
What happens when a force is applied below the center of mass in a system?
The system rotates counterclockwise.
What is the relationship between the center of gravity and the center of mass?
The center of gravity coincides with the center of mass.
What happens when an extended object is pivoted at its center of gravity?
It balances in any orientation.
How can the center of gravity of an irregularly shaped object be determined?
By suspending the object first from one point and then from another.
What is the method described in Figure 9.16 to determine the center of gravity of a wrench?
Hanging the wrench from two different points and drawing vertical lines.
Where is the center of gravity located in relation to the thickness of the wrench?
Halfway through the thickness of the wrench.
What happens if a wrench is hung freely from any point?
The vertical line through that point passes through the center of gravity.
What does it mean for g S to be constant over the mass distribution?
The value of g S is the same at all points in the mass distribution.
What is the significance of the center of gravity and center of mass being the same?
It indicates that the mass is equally distributed around the center of gravity.
True or false: The center of mass of a system can be described as the average position of the system's mass.
True
True or false: If a force is applied at the center of mass of a system, the system moves in the direction of the force without rotating.
True
True or false: The center of mass of a system is always located at the exact midpoint between two particles.
False
True or false: The translational motion of the center of mass of a system depends on other motions like rotation or vibration.
False
True or false: The center of mass of an object can be located by finding the point where the mass is concentrated.
True
True or false: The center of mass and center of gravity of an object are always located at the same point.
True
True or false: The center of gravity and center of mass always coincide in an extended object.
True
True or false: If an extended object is pivoted at its center of gravity, it will balance in any orientation.
True
True or false: The center of gravity of an irregularly shaped object can be determined by suspending the object from one point and drawing a vertical line.
True
True or false: In Figure 9.16, the center of gravity of the wrench is located at the intersection of the two vertical lines.
True
True or false: The vertical line through any point on a freely hanging wrench must pass through the center of gravity.
True
True or false: The translational motion of the center of mass depends on other motions like rotation or vibration.
False
True or false: The center of mass of a system consisting of two particles connected by a rigid rod is located at the midpoint of the rod.
True
True or false: The center of gravity and center of mass are always the same in every system.
False
True or false: The x coordinate of the center of mass of two particles on the x axis is given by x_CM = (m_1x_1 + m_2x_2) / (m_1 + m_2)?
True
True or false: The center of mass of a system of many particles in three dimensions is defined by the equations x_CM = (m_1x_1 + m_2x_2 + m_3x_3 + ... + m_nx_n) / (m_1 + m_2 + m_3 + ... + m_n), y_CM = (m_1y_1 + m_2y_2 + m_3y_3 + ... + m_ny_n) / (m_1 + m_2 + m_3 + ... + m_n), z_CM = (m_1z_1 + m_2z_2 + m_3z_3 + ... + m_nz_n) / (m_1 + m_2 + m_3 + ... + m_n)?
True
True or false: The position vector of the center of mass of a system of many particles is given by r_CM = (x_CMi^ + y_CMj^ + z_CM*k^)?
True
True or false: The x coordinate of the center of mass of an extended object with continuous mass distribution can be approximated by x_CM = (1/M) * ∫(x * dm)?
True
True or false: The center of mass of a uniform rod lies in the rod, midway between its ends?
True
True or false: The center of mass of a sphere or a cube lies at its geometric center?
True
Which of the following best describes the center of mass of a system?
The center of mass is the average position of the system's mass.
True or false: The translational motion of the center of mass of a system depends on other motions like rotation or vibration.
False
What happens when a force is applied above the center of mass in a system?
The system rotates clockwise.
True or false: The center of gravity and center of mass always coincide in an extended object.
False
What is the relationship between the center of gravity and the center of mass?
The center of gravity is always located below the center of mass.
True or false: The center of mass of a system consisting of two particles connected by a rigid rod is located at the midpoint of the rod.
False
Which statement is true about the center of gravity and the center of mass?
The center of gravity and the center of mass can be determined by suspending an object from different points.
What happens when an extended object is pivoted at its center of gravity?
The object remains balanced in any orientation.
How can the center of gravity of an irregularly shaped object be determined?
By locating the intersection of two vertical lines.
What is the relationship between the center of gravity and the center of mass?
The center of gravity and the center of mass are always located at the same point.
What is the significance of the center of gravity and center of mass being the same?
The object is in equilibrium.
What happens if a wrench is hung freely from any point?
The wrench remains balanced and the vertical line through the hanging point passes through the center of gravity.
What does it mean for g S to be constant over the mass distribution?
The mass distribution is uniform.
Where is the center of gravity located in relation to the thickness of the wrench?
Halfway through the thickness of the wrench.
Which equation describes the x coordinate of the center of mass of a system of many particles in three dimensions?
$x_{CM} = \frac{m_1x_1 + m_2x_2 + m_3x_3 + ... + m_nx_n}{m_1 + m_2 + m_3 + ... + m_n}$
What happens when a force is applied above the center of mass in a system?
The system rotates counterclockwise.
What is the relationship between the center of gravity and the center of mass?
They are always located at the same point.
What is the equation for the x-coordinate of the center of mass of two particles on the x axis?
$x_{CM} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$
What happens when a force is applied below the center of mass in a system?
The system rotates clockwise.
What is the equation for the x coordinate of the center of mass of an extended object with continuous mass distribution?
$x_{CM} = \frac{1}{M} \int (x \cdot dm)$
Test your knowledge on the center of mass and its role in describing the overall motion of a system. This quiz covers topics such as translational motion and mass distribution.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
