# Solving the Merry Go Round Problem Using Conservation of Angular Momentum

• phy21050
In summary, the problem involves a merry-go-round with a moment of inertia of 1000 kgm^2 and an initial angular velocity of 2.20 rad/s. When an 80kg man steps onto the rim, 2m away from the axis of rotation, the angular velocity decreases. The solution can be found using the conservation of angular momentum, and the man can be treated as a point mass for this purpose.

#### phy21050

Could someone walk me through the steps of the following problem step by step? Thanks. A merry go round with a moment of inertia of 1000kgm^2 is coasting at 2.20 rad/s. When an 80kg man steps onto the rim , a distance of 2 m from the axis of rotation the angular velocity decreases to ? rad/s

Hi,

I would like to see how you would start this problem before telling you any detailed steps. Here is what you should be thinking about.

1. What shape can the merry-go-round be approximated as?
2. What can the man be approximated as?
3. What law of physics can be used to deterimine the initial and final angular velocities?

For #3, think about what quantity you learned in class lately that involve angular velocities. Is that quantity conserved? If so, can you use it here?

thats partly the reason I am writing because the textbook sux and lecture for the most part has been not helpful so being that I have a difficult time as it is with Physics that only makes it more difficult. As for the answers to your questions...
1. the merry go round is like a circle
2. I have no idea what the man is, a mass?
3. and for the 3rd I am not sure

Originally posted by phy21050
1. the merry go round is like a circle

Yes. Now, you know the rotational inertia of the merry-go-round, and you know the expression for the rotational inertia of a circle (from your book).

2. I have no idea what the man is, a mass?

Yes, he's a mass, but we are also interested in the configuration of the system (that's how you find the rotational inertia). So, try to find the rotational inertia of the (man+merry-go-round). I would treat the man as a point mass for this purpose.

3. and for the 3rd I am not sure

This should be readily apparent from the same chapter in which the problem appears. Try to look for it.

could you help me with the problem Tom? I don't really have the slightest idea as where to begin. The question is on a take home assignment and there is not really a similar question in the book.

I am trying to help you with the problem, but to be honest it sounds like you want me to do it for you. Could you try to read the chapter and come up with *something*? This problem is really not that difficult.

Here's a hint: The conservation law I alluded to earlier is the conservation of angular momentum. This is one of the most important principles in physics, and I am sure that your teacher must have given special attention to it.

Give it a try, show me how you start the problem, and I will help you from there.

We can solve this problem by using the conservation of angular momentum.

The initial angular momentum at the instant the man is about to jump on is:

L(total=L(man)-L(mgr)=Rp(man)-I(mgr)*omega(initial)

Now try to find the angular momentum after he jumps on.

L(total)=I(total)*omega(final)=
(I(mgr)+m(man)*R^2)*omega(final)

You should be able to work through this problem now.
Just remember what you are trying to solve for.
You are trying to solve for the final angular momentum.

*Hint* In order to get the decrease(in angular speed)what has to be equal?

peace out M2k

## 1. What is the "Merry go round problem"?

The "Merry go round problem" is a physics problem that involves a person standing on a rotating platform, such as a merry-go-round or a rotating playground equipment. It explores the concept of centripetal force and how it affects the motion of objects on a rotating surface.

## 2. How does centripetal force play a role in the "Merry go round problem"?

Centripetal force is the force that keeps an object moving in a circular path. In the "Merry go round problem", the force that keeps the person on the rotating platform is the centripetal force. This force is directed towards the center of the rotation and is responsible for the circular motion of the person.

## 3. Why does the person on the "Merry go round" feel like they are being pushed outwards?

This feeling is caused by the centripetal acceleration, which is the acceleration towards the center of rotation. As the person moves in a circular path, they experience a change in direction and velocity, resulting in a force that feels like it is pushing them outwards.

## 4. How does the speed of the "Merry go round" affect the "Merry go round problem"?

The speed of the "Merry go round" affects the magnitude of the centripetal force. As the speed increases, the centripetal force also increases, making it more difficult for the person to maintain their position on the rotating platform. This can also affect the feeling of being pushed outwards.

## 5. What other factors can affect the "Merry go round problem"?

Other factors that can affect the "Merry go round problem" include the radius of the rotating platform, the mass of the person, and the coefficient of friction between the person's feet and the platform. These factors can impact the magnitude of the centripetal force and the person's ability to maintain their position on the rotating platform.