In this article, we will discuss the concept of circular motion. Objects (cars etc.) or people generally move around a circular track at different speeds, and they begin from a particular point either in the same direction or in the opposite direction.

The basic objective of this concept is generally to calculate:

- The time of meeting of people (running around the track) at the starting point again after they started.
- Meeting for the first time anywhere on the track.
- At how many different points do people meet while running on the circular track?

The time of their meeting again at the starting point will be the LCM of 120/12 & 120/20 i.e. 10 & 6 LCM of 10 and 6= 30

So, after 30 mins these people will be together at the starting point.

To check whether your answer is right or not

Calculate the position of A and B after 30 mins.

Calculate the position of A and B after 30 mins.

After 30 minutes, A would have taken 3 rounds and B would have taken 30/6 = 5 rounds. So after completing 3 & 5 rounds they will be at the starting point.

If 2 people have to meet for the first time, the faster person has to complete one full round extra over the slower person. The faster person is ahead of the slower one right from the first minute only due to his speed being higher than the speed of the other and they both are moving in the same direction.

It can be said that when the faster is ahead of the slower by one full track length, he will be overtaking the slower person from behind. Now, at this very moment these people meet.

In order to calculate the time we can say that time of meeting

= (track length/relative speed)

It can be said that when the faster is ahead of the slower by one full track length, he will be overtaking the slower person from behind. Now, at this very moment these people meet.

In order to calculate the time we can say that time of meeting

= (track length/relative speed)

Time of meeting = 120/(20 - 12) = 120/8 = 15min.

In order to visualize we can say that B covers 8 mtr/min extra over A. So when B covers 120 mtrs. extra he will overtake A from the behind and hence they both will meet.

The logic that operates behind calculating this is that if we divide the time of their first meeting at the starting point with the time of their first meeting anywhere on the track, we get the number of points at which these people would meet including the starting point.

Number of points = 30/15 = 2 points

This is inclusive of the starting point.

So far, we have solved the 3 types of problems taking 2 people A and B.

The immediate question that comes to our mind is what if more than 2 people are given?

How will we then solve the question?

The above concepts are applicable for more than 2 people/objects as well.

The immediate question that comes to our mind is what if more than 2 people are given?

How will we then solve the question?

The above concepts are applicable for more than 2 people/objects as well.

Must Read Time, Speed and Distance Articles

- Time, Speed and Distance: Basic concepts
- Time, Speed and Distance- Basics
- Time, Speed and Distance: Problems on Trains

- Time, Speed, Distance: Circular Motion
- Time, Speed and Distance- Ratio Concept
- Relative Speed & Problems on Trains

First calculate the following:

T_{ab}= Time in which B overlaps A or A overlaps B

T_{ac}= Time in which C overlaps A or A overlaps C

Then take the LCM of these two and you'll get the time of their 1^{st} meeting.

T

T

Then take the LCM of these two and you'll get the time of their 1

First calculate the following:

T_{a}= Time taken by A to complete the entire circular path.

T_{b}= Time taken by B to complete the entire circular path.

T_{c}= Time taken by C to complete the entire circular path.

T

T

T

L.C.M of these three times will give you the time at which A, B and C meet at the starting point for the 1^{st} time.

Similarly, we can apply the same concept for more than 3 objects as well.

Time taken to meet for the 1

Now P's speed = 20m/s and Q's speed=20 m/s.

Time taken to meet for the 2^{nd} time= 400/(20+20) = 10 sec.

Time taken to meet for the 2

Now P's speed =40 m/sec and Q's speed = 10 m/sec.

Time taken to meet for the 3^{rd} time= 400/(10+40)=8 sec.

Time taken to meet for the 3

Therefore, Total time= (8+10+8) = 26 seconds.

Let A be moving at a speed of 7kmph, B at 11kmph and C at 15kmph.

A and B meet at (11-7) points = 4 points.

B and C meet at (15-7) points=8 points.

HCF of 4, 8 will be 4.

Hence, the three meet at 4 points.