Basic application of “velocity”

I'm a basic learner.

I have been taught:

If anything is moving around in a circular path, it's velocity is zero.

I want to know that what the velocity really is, what its purposes are.

Tell me the differences between velocity and speed with real life examples, apart from the few given in the textbook for rote.

Thank you.

• Are you familiar with vectors? – Spencer Mar 19 at 12:32
• If it's moving at all, then velocity can't be zero. Average velocity, perhaps? – Arthur Mar 19 at 12:34
• Instantaneous velocity is nonzero. Average velocity taken over one circular orbit is zero. – Deepak Mar 19 at 12:39
• You've been taught wrong. What is true is that in uniform circular motion, the rate of change of speed (tangential acceleration) is $0$, because the tangential velocity (speed) is constant. – learner Mar 19 at 12:48
• Did my answer make sense to you or is there something which still needs clarification? – Spencer Apr 17 at 2:03

First you must understand the difference between displacement and distance.

The displacement of an object is the difference between it's initial position and its final position. This is represented by a displacement vector which points from the initial position to the final position. If the initial and final positions are the same then the displacement is $$0$$.

Distance is literally just to total number of meters you have traveled through. For each step you take, to increase the total distance you have traveled. This is what the odometer in a car measures.

To appreciate the distinction I am going to give you a simple 1-Dimensional example.

Bob walks to the right 5 meters, then he walks to the left 7 meters, finally he walk to the right 3 meters. What is Bob's total displacement? What is the total distance traveled by Bob?

We will represent Bob's position on a number line.

We can model each displacement to the right as a positive number, and each displacement to the left as a negative number. Bob's total displacement is then $$\Delta x = +5\ m - 7 \ m + 3\ m = + 1 \ m$$. In other word's Bob's displacement vector is $$1\ m$$ to the right.

Bob's total distance traveled is just the sum of all the distances he traveled through. $$d = 5\ m + 7\ m + 3\ m = 15\ m$$. Note that the distance is always represented as a positive number.

Now the average velocity of an object is just its total displacement divided by the amount of time for the motion. Similarly the average speed is the total distance traveled divided by the amount of time for the motion. Now we will apply what we have learned to the example you gave in the problem.

Bob runs one lap around a circular track of radius $$R$$ in an amount of time $$T$$.

What distance did Bob travel through? Well he ran one lap, which is a circumference of the circle. Therefore $$d=2\pi R$$. Bob's average speed is now calculated by dividing the distance travelled by the time.

$$Average\ Speed = \frac{2\pi R}{T}$$

What is Bob's total displacement? Well Bob finished his motion at the same place he started. This means that his final position and his initial position is the same. The displacement vector must have a length of $$0\ m$$ because it points from the same point to itself. Therefore $$\Delta \vec{x} = 0$$. Finally we compute the average velocity by dividing the displacement by the amount of time.

$$Average\ Velocity = \frac{0\ m}{T} = 0\ \frac{m}{s}$$