Understanding Momentum and Moment of Area Concepts | Explained by Experts

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In summary, the conversation discusses the difference between the momentum of the center of mass of a system and the sum of the independent momentums of every object in the system. The person asking the question also mentions not understanding the concepts of the first and second moment of area. Another person suggests that there may have been an error in the calculations and advises the person to provide more details about the problem in order to determine where the mistake was made. The conversation ends with the person realizing their mistake and asking for an explanation as to why their method was incorrect.
  • #1
Red_CCF
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Hi

I was wondering if anyone could explain why the momentum of the center of mass of a system is different than the sum of the independent momentums of every object.

I also don't understand the concepts of the first and second moment of area. I would appreciate it if someone explained it to me.

Thanks for any help that you can provide
 
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  • #2
Red_CCF said:
I was wondering if anyone could explain why the momentum of the center of mass of a system is different than the sum of the independent momentums of every object.
Why do you think it's different?
 
  • #3
Doc Al said:
Why do you think it's different?

Because on a question for my homework, which asked for linear momentum of the system, I got two different answers when i did the momentum of each separately than doing the momentum of the center of mass.
 
  • #4
Red_CCF said:
Because on a question for my homework, which asked for linear momentum of the system, I got two different answers when i did the momentum of each separately than doing the momentum of the center of mass.
I'd have to see the details, but I suspect you made an error.
 
  • #5
Doc Al said:
I'd have to see the details, but I suspect you made an error.

If they are indeed the same then I probably did. I'll try to work out what I did wrong. Thanks.
 
  • #6
Red_CCF said:
If they are indeed the same then I probably did. I'll try to work out what I did wrong. Thanks.

I think I figured out what I did but I don't really understand why. I did the change in position of the center of mass, divided it by the time interval, and multiplied the result by the total mass of the system and I got a very off answer. Can anyone explain why I can't do it this way? Thanks
 
  • #7
Red_CCF said:
I think I figured out what I did but I don't really understand why. I did the change in position of the center of mass, divided it by the time interval, and multiplied the result by the total mass of the system and I got a very off answer. Can anyone explain why I can't do it this way? Thanks
You can do it that way. In order to find out where you went wrong, please describe the actual problem.
 

FAQ: Understanding Momentum and Moment of Area Concepts | Explained by Experts

What is momentum and how is it related to the concept of moment of area?

Momentum is a physical quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity. Moment of area, on the other hand, is a measure of an object's resistance to rotation about a specific axis. These two concepts are related because the moment of area is used to calculate the angular momentum of an object.

How is momentum and moment of area used in real-world applications?

Momentum and moment of area are used in many real-world applications, such as engineering, physics, and sports. In engineering, they are used to design structures and machines that can withstand rotational forces. In physics, they are used to understand the motion of objects in space. In sports, they are used to analyze the movements of athletes and improve their performance.

What is the difference between linear momentum and angular momentum?

Linear momentum refers to the motion of an object in a straight line, while angular momentum refers to the motion of an object around a fixed point or axis. Linear momentum is calculated by multiplying an object's mass and velocity, while angular momentum is calculated by multiplying its moment of inertia and angular velocity.

How do you calculate the moment of area of an object?

The moment of area of an object is calculated by multiplying the force applied to the object and the distance from the axis of rotation. This can be represented by the equation M = Fd, where M is the moment of area, F is the applied force, and d is the distance from the axis of rotation.

Can you explain the concept of moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. Objects with a higher moment of inertia require more force to change their rotational motion, making them more stable.

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