Clear misconception: Angular Momentum of Merry Go Round vs Ice Skater

[fignewtons]

Homework Statement

Why is it that the horse closest to the axis of rotation on a merry go round spins slower than the horse on the outer edges of the merry go round?
I saw this video on youtube and got confused at the first merry go round example:


According to conservation of mass, isn't v inversely related to r, so shouldn't the inner horse spin faster? In the same way that ice skaters extend their arms to spin slower and pull in their arms to spin faster?

Please explain, thanks! Feel free to use math, examples, etc.

 

[gneill]

Homework Statement

Why is it that the horse closest to the axis of rotation on a merry go round spins slower than the horse on the outer edges of the merry go round?
I saw this video on youtube and got confused at the first merry go round example:


According to conservation of mass, isn't v inversely related to r, so shouldn't the inner horse spin faster? In the same way that ice skaters extend their arms to spin slower and pull in their arms to spin faster?

Please explain, thanks! Feel free to use math, examples, etc.

Conservation of mass isn't relevant. Perhaps you're thinking of conservation of angular momentum?

Unlike for your figure skater example, no mass is moving inwards or outwards to or from the axis of rotation; the horses are at fixed distances from the center. So conservation of angular momentum doesn't apply (or rather it isn't relevant) to your problem.

What applies is rotational velocity and how the linear (tangential) speed of the horse depends upon its distance from the center of rotation. You should agree that all the horses make a complete circuit in the same amount of time (since they're fixed to a rigid platform which turns at a given rate). But the total distance traveled by each horse differs depending upon the circumference of the circle it follows at its given radial distance. What's the formula for the circumference of a circle? The more distance it covers in the same amount of time, the faster its linear speed.