KE constant in circular motion?

[LanguageNerd]

I was just wondering how the kinetic energy in, for example, a car undergoing circular motion is constant. We know that it's constantly acceleration due to the constant change in velocity, but surely that means that in the KE equation (1/2mv^2) the velocity is constantly changing as well. This would mean that the KE is also constantly changing, no?

Thanks for any help in advance!

 

[adjacent]

Kinetic energy is a scalar quantity. It does not have a direction. So nothing will change. Since the magnitude of the velocity is constant, kinetic energy will stay the same.

 

[LanguageNerd]

But how can it be a scalar quantity when it contains a vector quantity?

 

[xibeisiber]

But how can it be a scalar quantity when it contains a vector quantity?

the inner product of two vector quantity is certainly a scalar quantity..
$\vec{v}\cdot\vec{v}$

 

[LanguageNerd]

Brilliant. Thanks all!

 

[Philip Wood]

A nit-pick… For a body going in a circle at constant speed, the acceleration isn't constant. Its magnitude is constant, but its direction keeps changing, because it's radial, and the particular radius keeps changing!

 

[adjacent]

and the particular radius keeps changing!

What do you mean by this? The radius of circular rotation is changing?

 

[Doc Al]

What do you mean by this? The radius of circular rotation is changing?

Think of the radius as a vector from the center to a particular point on the circle. It changes as you move around the circle.

At any point, the radial acceleration points toward the center of the circle (opposite to the radius vector at that point). That direction changes as you move around the circle.

 

[adjacent]

Think of the radius as a vector from the center to a particular point on the circle. It changes as you move around the circle.

At any point, the radial acceleration points toward the center of the circle (opposite to the radius vector at that point). That direction changes as you move around the circle.

Oh. I thought he said that the radius(Length) is changing :shy:

 

[Philip Wood]

He ought to have been clearer!

 

[Doc Al]

He ought to have been clearer!