# Why is 'the velocity' in circular motion changing?

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## Main Question or Discussion Point

Why is the velocity in circular motion changing, why not constant?

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kuruman
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Because velocity is a vector that has direction. The direction is changing so the vector is changing.

CWatters
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Velocity is a vector that has components speed and direction.

Change speed or direction and velocity changes.

In addition any change to velocity implies an acceleration.

'
Velocity is a vector that has components speed and direction.

Change speed or direction and velocity changes.

In addition any change to velocity implies an acceleration.
As you said above 'Change speed or direction and velocity changes.
So, in constant speed or velocity, we can not change direction or If we change direction, the velocity would change? say, If we drive a car at a constant speed (40km/hr), can't we change the direction?

jbriggs444
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'
If we drive a car at a constant speed (40km/hr), can't we change the direction?
Certainly we can. And doing so will change the velocity.

CWatters
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A constant speed does not imply a constant direction (Because speed does not have a direction component).

Velocity has components speed and direction. Constant velocity implies both components are constant.

So a car driving in a circle can have a constant speed but not a constant velocity.

CWatters
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Consider an aeroplane flying north at 100mph. It's speed is 100mph. It's velocity is 100mph North.

If it turns around and heads South at 100mph it's speed is still 100mph. It's velocity has changed to 100mph South.

Mister T
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Why is the velocity in circular motion changing, why not constant?
Draw an arrow representing the velocity of a particle and label it $\vec{v}_1$. Then do it again, some time $\Delta t$ later, for that same particle and label it $\vec{v}_2$. If the particle is moving with uniform circular motion your two arrows have the same length. But in general they point in different directions. Can you now draw on your diagram an arrow representing $\Delta\vec{v}$ such that $\vec{v}_1+\Delta \vec{v}=\vec{v}_2$.

If you can see why $\Delta \vec{v}$ is not zero then you have shown that the acceleration $\vec{a}$ cannot be zero since $\vec{a}\approx\frac{\Delta \vec{v}}{\Delta t}$ for small $\Delta t$.

You can see diagrams illustrating this, accompanied by explanation, in any introductory physics textbook. If the one you see is not to your liking, find a different textbook. There are lots of them out there, many of them are free.

kuruman