# General question about momemtum / motion

I do not have a Physics or science background. I have a question which is related to physics and I am sure this is the right forum for the answer.

Imagine a big circle with a radius of 10cm and in the middle of the big circle there is a small circle with a radius of 3cm. Inside small circle at the center there is house, small circle can be referred as a boundary of the house and large circle can be referred as a open field around the house.

Question : If person A standing at a edge of small circle and person B standing exact in the same position but on the edge of the open field that is circle B. If they both starts walking (at the same speed) to take a round of the house. The person walking inside will finish faster coz he has to cover less distance….. What if I connect person A and person B with a long STICK and then they start walking simultaneously at same speed. I am sure after few steps there will be misalignment between them and person A will be ahead of person B.

If this is the case, imagine the big circle as a Clock and house a centre of the clock where “Seconds” hand is fixed. The clock hand for “Seconds” is in same position where A and B was standing. Now I replace A and B with 2 pencils fixed on “Seconds” hand in the same position where A and B were standing, pointing the pencil tip on the surface of the clock. Now if the “Seconds” hand starts moving , there is no reason to NOT believe that both circles will be drawn at the same time, in other words person A and person B taking same amount of time to circle the house. I don’t understand why different result for similar scenarios. Am i wrong in assumptions. ?? For the first senario :

Question : If person A standing at a edge of small circle and person B standing exact in the same position but on the edge of the open field that is circle B. If they both starts walking (at the same speed) to take a round of the house. The person walking inside will finish faster coz he has to cover less distance….. What if I connect person A and person B with a long STICK and then they start walking simultaneously at same speed. I am sure after few steps there will be misalignment between them and person A will be ahead of person B.

Here when you say "If they both starts walking (at the same speed)", I assume you are talking about linear velocity and not angular velocity.. In that case, you speculation is correct. There will be a misalignment after sometimes, because the person on the outer circle will have a lesser angular velocity than the person on the smaller circle.

No problem here.

But for the second scenario :

If this is the case, imagine the big circle as a Clock and house a centre of the clock where “Seconds” hand is fixed. The clock hand for “Seconds” is in same position where A and B was standing. Now I replace A and B with 2 pencils fixed on “Seconds” hand in the same position where A and B were standing, pointing the pencil tip on the surface of the clock. Now if the “Seconds” hand starts moving , there is no reason to NOT believe that both circles will be drawn at the same time, in other words person A and person B taking same amount of time to circle the house.

Here you are saying that you fixed the pencils on the seconds hand of the clock. and by doing this, you are making the angular velocity of two pencils same cause they are fixed to the same rotating hand. thus in this case, the outer circle pencil will have a greater linear velocity than the inner one because

## V = wr (where w = angular velocity and r = radius)

Hence there is no problem if the outer circle and inner circle gets drawn at the same time.

• Thanks Anubhav, for the first scenario I meant by angular velocity since both A and B will walk around the circle to complete the round. What would happen then ? – Logical Indian Aug 3 '19 at 22:01
• @LogicalIndian Well if you meant the angular velocity to be same in the first case, then there will be no misalignment of the sticks .. – g2m37 Aug 4 '19 at 4:59
• How is that possible ? circumference of outer circle is bigger than inner circle. while walking A on the inner circle will be ahead of B. So there will be misallignment in few steps. – Logical Indian Aug 5 '19 at 0:32
• Well angular velocity means the angle swiped/angular displacement per unit time, so if the angle swiped is same, then there will be no misalignment because distance = radius*theta – g2m37 Aug 6 '19 at 4:10