Does Zero Linear Momentum Always Mean Zero Kinetic Energy?

In summary, if the kinetic energy of a system of particles is zero, then the linear momentum of that system is also zero. However, the reverse is not always true. This means that if the linear momentum of a system of particles is zero, the kinetic energy may not necessarily be zero. This applies to both linear and angular momentum. For example, if two particles with equal mass but opposite velocities (+v and -v) collide and come to a stop, the momentum is zero but the kinetic energy is not. On the other hand, if the kinetic energy is zero, it implies that the total mass of the system is at rest, but the individual particles may still have non-zero momentum. This can be seen in the equation KE =
  • #1
AdityaDev
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"if kinetic energy of system of particles is zero, then linear momentum of that system of particles is zero but the reverse is not true. That is if linear momentum of a system of particles is zero, then the kinetic energy may not be zero"

This is what I got from my text. Can you provide me with some examples because I am a bit confused. Can you provide some explanation?
Is this true for angular momentum?
 
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  • #2
Consider two particles with mass m, one with velocity +v and one with velocity -v.
 
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  • #3
Vanadium 50 said:
Consider two particles with mass m, one with velocity +v and one with velocity -v.
So momentum is zero and kinetic E is not zero. Can you give an example for kinetic energy zero and momentum non zero?
 
  • #4
AdityaDev said:
So momentum is zero and kinetic E is not zero. Can you give an example for kinetic energy zero and momentum non zero?
KE = sum of 1/2 mv2. Can any of those terms be negative?
Or, imagine covering the whole system with a curtain or box and treating it as one object of total mass M and velocity V.
P=MV, while KE= 1/2MV2+ KE(within system, relative to the center of mass)
If KE = 0, what does that imply? Assume masses are never negative.
 
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  • #5

1. What is momentum and kinetic energy?

Momentum is a measure of an object's motion, calculated by multiplying its mass by its velocity. Kinetic energy is the energy an object possesses due to its motion, calculated by multiplying its mass by half of its velocity squared.

2. How are momentum and kinetic energy related?

Momentum and kinetic energy are both measures of an object's motion and are directly proportional to each other. This means that as an object's momentum increases, so does its kinetic energy.

3. What is the difference between linear and angular momentum?

Linear momentum refers to the motion of an object in a straight line, while angular momentum refers to the motion of an object around an axis or point. Linear momentum is calculated by multiplying an object's mass by its linear velocity, while angular momentum is calculated by multiplying its moment of inertia by its angular velocity.

4. How is momentum conserved in a closed system?

In a closed system, the total amount of momentum remains constant. This means that if one object in the system gains momentum, another object in the system must lose an equal amount of momentum. This principle is known as the law of conservation of momentum.

5. How does kinetic energy affect an object's ability to do work?

Kinetic energy is the energy an object possesses due to its motion, and it is directly related to an object's ability to do work. This means that the more kinetic energy an object has, the more work it can do. For example, a moving object can use its kinetic energy to push or lift other objects.

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