Center of Mass

Definition

The center of mass is the point at which an object's entire mass can be considered to be concentrated. It is the average position of the mass of an object, and it is the point around which the object's rotation and motion can be analyzed.

5 Must Know Facts For Your Next Test

1. The center of mass of an object is the point at which the object's entire mass can be considered to be concentrated, and it is the point around which the object's rotation and motion can be analyzed.
2. The center of mass of a rigid body is the average position of the mass of the object, and it is the point at which the object's weight can be considered to act.
3. The center of mass of a system of particles is the weighted average of the positions of the individual particles, where the weights are the masses of the particles.
4. The center of mass of an object is important in the analysis of linear momentum, impulse, and collisions, as well as in the analysis of static equilibrium and the motion of pendulums.
5. The location of the center of mass of an object can be determined experimentally or calculated using the object's geometry and the distribution of its mass.

Review Questions

• Explain how the concept of center of mass is used in the analysis of linear momentum and impulse.
  • The center of mass of an object is the point at which the object's entire mass can be considered to be concentrated. This is important in the analysis of linear momentum and impulse because the linear momentum of an object is the product of its mass and its velocity, and the impulse acting on an object is the change in its linear momentum. By considering the center of mass of an object, the analysis of linear momentum and impulse can be simplified, as the object's motion can be analyzed as if all of its mass were concentrated at a single point.
• Describe how the center of mass of an object is used in the analysis of static equilibrium.
  • The center of mass of an object is the point at which the object's weight can be considered to act. This is important in the analysis of static equilibrium because for an object to be in static equilibrium, the net force and the net torque acting on the object must be zero. By considering the location of the center of mass, the analysis of the forces and torques acting on the object can be simplified, as the weight of the object can be treated as a single force acting at the center of mass.
• Explain how the concept of center of mass is used in the analysis of the motion of pendulums.
  • The center of mass of a pendulum is the point around which the pendulum rotates. This is important in the analysis of the motion of pendulums because the motion of a pendulum can be described by the rotation of the pendulum about its center of mass. By considering the location of the center of mass, the analysis of the forces and torques acting on the pendulum can be simplified, and the period of the pendulum's oscillation can be determined using the pendulum's length and the acceleration due to gravity.

Related terms

Centroid: The centroid is the geometric center of an object, which may or may not coincide with the object's center of mass.

Moment of Inertia: The moment of inertia is a measure of an object's resistance to changes in its rotational motion, and it depends on the object's mass and the distribution of that mass around its center of mass.

Torque: Torque is the rotational force that causes an object to rotate around a specific axis, and it is calculated as the product of the force and the distance from the center of mass to the line of action of the force.