Kinetic Energy & Intrinsic Angular Momentum

[metastable]

I had a question about the equation (1/2)mv^2...

Why is the velocity squared? Why not simply (1/2)mv? Does it have anything to do with the intrinsic angular momentum ie does the intrinsic angular momentum change in anyway as velocity increases in a particular reference frame leading to the squaring of velocity in the (1/2)mv^2 KE equation?

 

[PeroK]

$mv$ is the magnitude of momentum.

There are a number of ways to derive the equation for kinetic energy. Have you looked online for one of them?

 

[metastable]

I have looked through the wikipedia article on KE, but still trying to understand why a doubling of velocity means a quadrupling of the energy.

 

[PeroK]

I have looked through the wikipedia article on KE, but still trying to understand why a doubling of velocity means a quadrupling of the energy.

Try this:

https://www.khanacademy.org/science...gy/kinetic-energy-ap/a/what-is-kinetic-energy

 

[metastable]

Try this:

https://www.khanacademy.org/science...gy/kinetic-energy-ap/a/what-is-kinetic-energy

Interesting article... it states:

• Kinetic energy depends on the velocity of the object squared. This means that when the velocity of an object doubles, its kinetic energy quadruples. A car traveling at 60 mph has four times the kinetic energy of an identical car traveling at 30 mph, and hence the potential for four times more death and destruction in the event of a crash.

So I understand a car traveling twice as fast has 4 times as much KE... but I'm not sure if it answers my original question...

Does it have anything to do with the intrinsic angular momentum ie does the intrinsic angular momentum change in anyway as velocity increases in a particular reference frame leading to the squaring of velocity in the (1/2)mv^2 = KE equation?

 

[PeroK]

Interesting article... it states:

• Kinetic energy depends on the velocity of the object squared. This means that when the velocity of an object doubles, its kinetic energy quadruples. A car traveling at 60 mph has four times the kinetic energy of an identical car traveling at 30 mph, and hence the potential for four times more death and destruction in the event of a crash.

So I understand a car traveling twice as fast has 4 times as much KE... but I'm not sure if it answers my original question...

Does it have anything to do with the intrinsic angular momentum ie does the intrinsic angular momentum change in anyway as velocity increases in a particular reference frame leading to the squaring of velocity in the (1/2)mv^2 = KE equation?

It has nothing to do with intrinsic angular momentum.

The page I linked to explained it all - unless you skipped over the maths!

 

[metastable]

If we use : W=m⋅d⋅((vf^2−vi^2) / 2d) from the article the velocity is squared as well. Perhaps I am asking a question with no real answer ie there is no "why..." it just is the way it is and there's an equation that describes it.

 

[PeroK]

If we use : W=m⋅d⋅((vf^2−vi^2) / 2d) from the article the velocity is squared as well. Perhaps I am asking a question with no real answer ie there is no "why..." it just is the way it is and there's an equation that describes it.

The derivation is reasonably elementary in that it only uses the concept of work = force x distance.

You can also look at it as follows. Imagine moving an object up in a gravitational field. As it moves it gains potential energy. In a uniform field it must gain the same energy for every $1m$ it is raised. Why? Because every $1m$ up is just the same as the $1m$ before and the $1m$ after.

The GPE (gravitational PE) must be proportional to the height it is raised. It turns out that it is $mgh$, but any constant times $mh$ would do.

You also have the kinematic formula $v^2 = 2gh$, which can be derived simply, for an object falling from rest under constant gravity.

Hence $v^2$ and not $v$ must be proportional to GPE. And, hence, you have $v^2$ in the formula for KE.

 

[Dale]

Also, early work studying the depth of indentions in soft clay showed that the depth was proportional to v^2.

I have no idea how angular momentum came into this thread. It is completely unrelated as far as I can see.