Center of Mass
For a system of particles, this is the single point that moves as if all the mass were concentrated there and all external forces acted there.
What is the center of mass?
For a system of particles, Newton’s second law connects the net external force to this quantity times the acceleration of the center of mass.
What is the total mass of the system?
This vector quantity is defined as mass times velocity.
What is linear momentum?
This quantity equals the change in momentum and is also the area under a force-versus-time graph.
What is impulse?
A rocket moves forward because it expels mass in this direction.
What is backward?
If you increase one object’s mass in a system while leaving the others fixed, the center of mass shifts in this direction.
What is toward the more massive object?
These forces cancel in pairs inside a system and therefore do not affect the motion of the system’s center of mass.
What are internal forces?
If an object’s velocity doubles while its mass stays the same, this happens to its momentum.
What is it doubles?
In any collision of an isolated system, this quantity is always conserved.
What is total linear momentum?
A rocket in deep space can speed up without pushing on air because its motion is explained by this conservation law.
What is conservation of momentum?
In an isolated system, internal forces can change the relative positions of objects, but they cannot change this motion of the center of mass.
What is its constant-velocity motion?
If the net external force on a system is zero, this quantity for the whole system must remain constant.
What is the total momentum?
A truck and a car move with the same speed. This vehicle usually has the greater momentum.
What is the truck?
In this type of collision, both momentum and kinetic energy are conserved.
What is an elastic collision?
In rocket motion, the rocket gains forward momentum while the expelled fuel gains this kind of momentum.
What is equal and opposite momentum?
A bat tossed into the air rotates wildly, but this point still follows a simple parabolic path if gravity is the only external force.
What is the center of mass?
A fireworks shell explodes in midair. The explosion forces are huge, but during the explosion they are mostly this type of force, so they do not change the motion of the center of mass.
What are internal forces?
Momentum points in this direction relative to an object’s motion.
What is the same direction as the velocity?
In this type of collision, the colliding objects stick together after impact.
What is a completely inelastic collision?
This is the key reason ordinary F=ma needs special care when applied directly to rockets.
What is that the mass of the rocket changes with time?
Two equal masses are at x=0 m and x=10 m. A third mass twice as large is at x=4m. This qualitative statement about the center of mass is true.
What is that the center of mass lies closer to x=4 m than to the midpoint of the two equal masses?
When analyzing a multi-object system, this is the best reason to treat all the objects as one combined system rather than separately.
What is to eliminate internal forces and focus only on external forces and total momentum?
An object can have large kinetic energy but small momentum, or vice versa, because kinetic energy depends on this power of speed while momentum depends on the first power.
What is the second power (speed squared)?
In a collision with no external force, kinetic energy may decrease, but this quantity cannot change.
What is total momentum?
If a rocket ejects exhaust faster relative to the rocket, this general effect happens to its ability to change speed.
What is it can achieve a greater change in speed?