Does the record move faster or ?

[Anonymous9001]

"Play a record on a record player. Draw a dot at a point on the outside of the record. Then draw a dot on the inner part of the record near the center, at the same level as the other dot.

Now draw a line on the record player as sort of a 'finish line' for the dot to cross when the record spins.

Play the record. As the record spins, both dots cross the 'finish line' at exactly the same time, even though the dot on the outside has a much longer distance to travel. Even though they're on the same record, it seems one dot is moving faster than the other, which is, of course, impossible."

Someone posted this online and I have struggled to understand why this is, I understand though that it's a simple concept but I do not know how to explain I suppose? It's indeed true the outside dot has a longer distance to travel while the inside has a shorter, and they're both moving at the same speed (I think?). Could anyone explain how this works?

Side note: This is not a homework question (as you can tell from the comment above it's not a question it's more of a statement for us to try out ourselves.

EDIT: I also have no idea where to post this, but I'm assuming this may be the right location.
I have attached a picture:
http://img809.imageshack.us/img809/7500/48043578.th.png

 

[Gordianus]

The paradox arises because you're comparing speed versus angular velocity.
The outer dot has greater speed because it travels a larger distance in a given time. However, both dots have the same angular velocity, because they make a full turn (360 degrees) in the same time.

 

[Anonymous9001]

Thank you for a quick and easy to understand answer; so the answer would be the following "The dots have the same angular velocity but the outside doth as a greater speed." if I read your comment right?

Thanks again!

 

[Gordianus]

Yeap.

 

[pmacias]

I can provide an explanation for this phenomenon using the principles of rotational motion and angular velocity.

When a record is played on a record player, it spins at a constant angular velocity. This means that every point on the record, whether it is near the center or on the outer edge, is moving at the same speed. This is because the record player applies a constant torque to the record, causing it to rotate at a constant rate.

In this scenario, the dots at different points on the record are essentially moving in circles of different radii. The dot on the outer edge has a larger radius and therefore has a longer distance to travel in one rotation compared to the dot near the center.

However, since they are both moving at the same angular velocity, they will both complete one rotation in the same amount of time. This is why they both cross the "finish line" at the same time.

To put it simply, the dot on the outer edge may be moving a longer distance, but it is also moving faster to cover that distance in the same amount of time as the dot near the center. This is similar to how a car on the outer lane of a racetrack may have a longer distance to travel, but it is also moving faster compared to a car on the inner lane.

In conclusion, the dots on the record are not actually moving at different speeds, but rather at the same angular velocity. It is just the distance they have to travel that makes it seem like one is moving faster than the other.