How is kinetic energy related to momentum in terms of velocity?

In summary, by differentiating kinetic energy with respect to velocity, the result is momentum. This can be physically explained through the derivation of energy conservation, where Newton's laws are integrated with respect to velocity. This results in kinetic energy on one side and potential energy on the other. This concept is related to the advanced concept of "conjugate momentum" in Lagrangian and Hamiltonian mechanics.
  • #1
xiankai
31
0
if you differentiate kinetic energy wrt. to velocity, you will get momentum as the result.

what i wanted to ask is that, how can this physically explained? that kinetic energy can be viewed as the rate of change of momentum for a change in velocity? is there any analogy?
 
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  • #2
The derivation of energy conservation is where this comes from. You start with Newton's laws, then integrate basically with respect to the velocity, and what comes out is the kinetic energy on the ma side and potential energy on the other side. That's why it comes out that way.
 

1. What is momentum and why is it important?

Momentum is a measure of an object's motion, calculated by multiplying its mass and velocity. It is important because it helps us understand and predict how objects will behave when they interact with each other.

2. How is momentum different from kinetic energy?

Momentum and kinetic energy are related but different concepts. Kinetic energy is a measure of an object's motion and is calculated by multiplying its mass, velocity, and the square of its velocity. Momentum only takes into account an object's mass and velocity.

3. How is momentum conserved in a closed system?

In a closed system, the total momentum remains constant. This means that the sum of the momentums of all the objects in the system before an interaction is equal to the sum of their momentums after the interaction. This is known as the law of conservation of momentum.

4. How does mass affect an object's momentum?

The greater the mass of an object, the greater its momentum will be. This means that a heavier object will have more resistance to changes in its motion and will require more force to accelerate.

5. Can an object have momentum without having kinetic energy?

Yes, an object can have momentum without having kinetic energy. This can occur in situations where an object is at rest or moving at a constant velocity. In these cases, the object's momentum is due to its mass and direction of motion, rather than its speed.

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