# velocity is zero if displacement is zero

#### brownt

Is it correct to that velocity is zero if displacement is zero? So, does travelling in a circle and beginning and ending at the same point, mean there was a velocity of zero?

Nope and nope.

#### Woody

Not Quite,

The velocity is changing as you go around the circle,
If split the circle into lots of little bits
and you add together all the velocities operating in each of those little bits,
you will find that the velocities going north will exactly match and cancel the velocities going south
The same will apply for those going east and west.

So although none of the actual velocities going round the circle are zero,
the total sum of all the velocities will be zero.

#### HallsofIvy

The average velocity will be 0 but the velocity at any time is not. Also, the average speed is not 0. Are your clear on the distinction between "velocity" and "speed" in physics?

#### brownt

The average velocity will be 0 but the velocity at any time is not. Also, the average speed is not 0. Are your clear on the distinction between "velocity" and "speed" in physics?
Yes, speed is scalar meaning magnitude only, and velocity is vector meaning it includes direction and magnitude.

I see, so the average velocity will be zero.

#### benit13

Just to be clear, the results for constant circular motion mentioned here:

1. "none of the actual velocities going round the circle are zero,
the total sum of all the velocities will be zero."

2. "The average velocity will be 0 but the velocity at any time is not. Also, the average speed is not 0."

Assumes that you are considering a single period*, where the object travels around the circle back to its start point. If you're not considering a single period, let us know because things can get a little bit more tricky.

*actually $$\displaystyle n$$ periods of circular motion, where n is a positive non-zero integer.

1 person

#### Woody

In general,
If the average velocity over a given time period is zero
then the average displacement over the same time period will be zero.

However the actual velocities and displacements over that time period might not be zero,
(You have been there, and come back again).