# Moment of inertia of a merry-go-round

• brendan3eb
In summary, the conversation discusses the use of the rotational inertia of a hoop instead of a disk in a problem involving a merry-go-round. The speaker initially thought the disk would be used, but the solution uses the hoop due to the mass being spread out at the outer edge, as seen in a traditional merry-go-round with horses. The conversation also mentions a similar spinning playground equipment that is no longer made for safety reasons.
brendan3eb
In a certain problem I was working on, it asks for the inertia of a merry-go-round, and my first instinct was that it would be the inertia of a disk about its central axis I=(1/2)MR^2, but the solution actually uses I = MR^2 the rotational inertia of a hoop about the central axis. Why do they choose the hoop and not the disk? There is nothing mentioned about how the mass is spread out, just that there is a merry-go-round.

The merry-go-round I picture have horses around the outer edge that the kids (or bigger kids!) sit on, so most of the mass is at the outer edge - hence a hoop.
It is a bit unfairly worded as a question though.

ahhh, yeah, see it said a merry-go-round at a playground so I was thinking of that thing where there are just bars extending from the center and you have to hold on as it spins really fast. I don't know what it is called but I thinked that they stopped making them for safety reasons. Those things were sweet and great examples of basic physics concepts.

Anyway, thanks for pointing that out. It makes more sense now.

## 1. What is the moment of inertia of a merry-go-round?

The moment of inertia of a merry-go-round is a measure of its resistance to rotational motion. It is a property of an object that depends on its mass distribution and the axis of rotation. In simpler terms, it is a measure of how difficult it is to change the rotation of the merry-go-round.

## 2. How is the moment of inertia of a merry-go-round calculated?

The moment of inertia of a merry-go-round can be calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. It can also be calculated by integrating the mass distribution of the object with respect to the axis of rotation.

## 3. What factors affect the moment of inertia of a merry-go-round?

The moment of inertia of a merry-go-round is affected by the mass distribution of the object, the shape of the object, and the position of the axis of rotation. Objects with more mass distributed farther from the axis of rotation will have a higher moment of inertia.

## 4. How does the moment of inertia affect the motion of a merry-go-round?

The moment of inertia affects the rotational motion of a merry-go-round by determining how quickly or slowly it will rotate in response to a force. Objects with a higher moment of inertia will rotate more slowly, while objects with a lower moment of inertia will rotate more quickly.

## 5. Can the moment of inertia of a merry-go-round be changed?

Yes, the moment of inertia of a merry-go-round can be changed by altering the mass distribution or the axis of rotation. For example, if the mass is moved closer to the axis of rotation, the moment of inertia will decrease, resulting in a faster rotational motion.

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