Calculating Final Angular Speed of a Rotating Disk with a Horizontal Axis

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Homework Help Overview

The problem involves a uniform vertical disk that rotates about a horizontal axis when a constant horizontal force is applied via a string. The disk starts from rest and is pulled until it completes a quarter revolution. The goal is to determine the final angular speed of the disk.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to initiate the problem and question the implications of applying a constant force to a rotating disk. There is discussion about the nature of angular acceleration and the conditions under which conservation laws may apply.

Discussion Status

Participants are exploring various aspects of the problem, including the effects of constant force and torque on angular acceleration. Some have raised questions about the application of conservation laws, particularly conservation of angular momentum, and the necessary conditions for their use. No consensus has been reached yet.

Contextual Notes

There is an emphasis on the non-constant nature of torque due to the changing perpendicular distance as the disk rotates. Participants are also considering the implications of frictionless conditions and the specific setup of the problem.

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Homework Statement


You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its center. Initially, the disk is at rest with the string connection at the highest point on the disk. You pull the string with a constant horizontal force F⃗ until the wheel has made exactly one-quarter revolution about a horizontal axis through its center, and then let go.

Find the final angular speed of the disk.

Homework Equations


v=r(omega)

The Attempt at a Solution



Not totally sure where to start?
 
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Do you know the answer to this problem? If so, can you post it?
 
As you have a constant force (F) and no friction, the disk will ... (?)
Now write the equations you know for (?)
Hth :)
 
The simplest type of angular motion problems have a constant torque, which results in a constant angular acceleration. In your problem, unless I am reading it wrong, the force is constant but the perpendicular distance to the axis of rotation is not constant. (The reason the perpendicular distance is not constant is because the point where the force is applied is rotating with the disk, but the direction of the force is not rotating with the disk - because it is specified in the problem that it is a constant HORIZONTAL force.) The result is an angular acceleration that is NOT constant. Any idea how you can find angular velocity from a varying angular acceleration?
 
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Replusz said:
As you have a constant force (F) and no friction, the disk will ... (?)
Now write the equations you know for (?)
Hth :)
Not sure where you were headed with that. If you were thinking in terms of linear forces and accelerations, there is also a non-constant force. If you were thinking in terms of torques and angular accelerations, as TomHart points out, the torque is not constant.
 
TomHart said:
Do you know the answer to this problem? If so, can you post it?
No, I do not know the answer.
 
ooohffff said:

Homework Equations

Any conservation laws that might apply?
 
haruspex said:
Any conservation laws that might apply?

Conservation of angular momentum?
 
ooohffff said:
Conservation of angular momentum?
What conditions do you need to be able to apply that? What reference point would you take as axis?
Any other laws?
 

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