Physics
Center of Mass
Center of Mass Motion
11
⚡ Quick Summary
The center of mass of a system moves as if all the mass is concentrated there and all external forces are applied at that point. If there's no external force, the center of mass remains at rest or continues to move with constant velocity.
x_CM = (m1x1 + m2x2) / (m1 + m2)
The position of the center of mass (CM) is given by a weighted average of the positions of the individual particles in the system. In the absence of external forces, the velocity of the center of mass remains constant. If the CM is initially at rest, it remains at rest.
Center of Mass
11
⚡ Quick Summary
The center of mass of a system is the average position of all the parts of the system, weighted by their masses.
Not explicitly stated in this section, but implied: Concept of weighted average
The center of mass is a point that represents the average location of the mass of an object or system. It's a useful concept for analyzing the motion of complex objects, as the motion of the center of mass often simplifies the analysis. When external forces act on a system, the center of mass moves as if all the mass of the system were concentrated at that point and the forces were applied there.
Linear Momentum
11
⚡ Quick Summary
Linear momentum is a measure of the mass in motion: how much 'stuff' is moving and how fast it's going.
p = mv (momentum = mass * velocity)
Linear momentum is a vector quantity defined as the product of an object's mass and its velocity. It is a conserved quantity in a closed system (one where no external forces act). This means that the total momentum of a system remains constant unless acted upon by an external force. The principle of conservation of momentum is fundamental to understanding collisions and explosions.
Kinetic Energy
11
⚡ Quick Summary
Kinetic energy is the energy of motion.
KE = (1/2)mv^2 (Kinetic Energy = 1/2 * mass * velocity^2)
Kinetic energy is the energy an object possesses due to its motion. It's directly proportional to the mass of the object and the square of its velocity.
Conservation of Momentum
11
⚡ Quick Summary
In a closed system, the total momentum before an event equals the total momentum after the event.
p_initial = p_final (total initial momentum = total final momentum)
The principle of conservation of momentum states that the total momentum of an isolated system (no external forces) remains constant. This is a direct consequence of Newton's laws of motion, particularly Newton's third law (action-reaction). It's a crucial concept for analyzing collisions, explosions, and other interactions between objects.