# KE constant in circular motion?

1. May 22, 2014

### 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!

2. May 22, 2014

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.

3. May 22, 2014

### LanguageNerd

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

4. May 22, 2014

### xibeisiber

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

5. May 22, 2014

### LanguageNerd

Brilliant. Thanks all!

6. May 23, 2014

### 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!

7. May 23, 2014

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

8. May 23, 2014

### Staff: Mentor

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.

9. May 23, 2014

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

10. May 23, 2014

### Philip Wood

He ought to have been clearer!

11. May 23, 2014

:rofl: