What is the new angular velocity when a man moves on a rotating merry-go-round?

In summary, the problem involves a man standing on a rotating merry-go-round and then moving to a different point. The new angular velocity is found by comparing the old and new moments of inertia and using the law of conservation of angular momentum. The correct answer is 0.569 rev/sec, assuming the merry-go-round is a solid cylinder with a mass of 25 kg and a radius of 2 m.
  • #1
BrainMan
279
2

Homework Statement


A merry-go-round rotates at an angular velocity of 0.2 rev/s with an 80 kg man standing at a point 2 m form the axis of rotation. what is the new angular velocity when the man walks to a point 1 m from the center? Assume the merry-go-round is a solid cylinder of mass 25 kg and radius 2 m.


Homework Equations


I= MR^2
L = Iω



The Attempt at a Solution



First I found the moment of inertia of the platform
25 x 4 = 100
Then I found the original moment of inertia of the man
80(4) = 320

Then I found the total angular momentum
L = (100 + 320)0.2/2pi
L = 42/pi

Then I found the moment of inertia after the man moved
I = 80(1)
I = 80

Then I compared the old momentum to the new momentum
42/pi = 180ω
ω = .074 rad/sec
.074 x 2pi = .467 rev/sec

The correct answer is .569 rev/sec
 
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  • #2
BrainMan said:
Assume the merry-go-round is a solid cylinder of mass 25 kg and radius 2 m....

I= MR^2

The problem said the merry-go-round was a solid cylinder, this is the incorrect moment of inertia.

Edit:
All your steps are good though; I walked through your own steps with the correct moment of inertia and got the correct answer.
 
Last edited:
  • #3
Nathanael said:
The problem said the merry-go-round was a solid cylinder, this is the incorrect moment of inertia.

Edit:
All your steps are good though; I walked through your own steps with the correct moment of inertia and got the correct answer.

I got it right. Thanks!
 

Related to What is the new angular velocity when a man moves on a rotating merry-go-round?

What is the Angular Momentum Problem?

The angular momentum problem is a concept in physics that arises when trying to calculate the angular momentum of a system. It is a problem because the concept of angular momentum is not well-defined or easily quantifiable, leading to difficulties in accurately measuring or predicting its value.

Why is the Angular Momentum Problem important?

The concept of angular momentum is crucial in understanding the behavior of rotating objects and systems in physics. It is used to explain phenomena such as rotational motion, gyroscopic stability, and the conservation of angular momentum. Therefore, the angular momentum problem is significant in helping scientists and researchers make accurate predictions and calculations in various fields of study.

What are some approaches to solving the Angular Momentum Problem?

One approach to solving the angular momentum problem is by using angular momentum operators in quantum mechanics. Another approach is by using classical mechanics and the laws of conservation of angular momentum. Additionally, numerical methods and computer simulations can also be used to solve the problem in more complex systems.

What are some real-world applications of the Angular Momentum Problem?

The angular momentum problem has numerous applications in real-world scenarios. It is used in the design and operation of satellites, rockets, and other spacecraft, as well as in the understanding of celestial mechanics and the motion of planets and galaxies. It is also essential in the development of technologies such as gyroscope and inertial navigation systems.

Are there any current research efforts to address the Angular Momentum Problem?

Yes, there are ongoing research efforts to better understand and solve the angular momentum problem. Some current research focuses on developing new mathematical models and theories to accurately describe the concept of angular momentum and its behavior in complex systems. Other efforts involve using advanced computational methods and technologies to simulate and analyze angular momentum in various scenarios.

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