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

[ooohffff]

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?

 

[TomHart]

Do you know the answer to this problem? If so, can you post it?

 

[Replusz]

As you have a constant force (F) and no friction, the disk will ... (?)
Now write the equations you know for (?)
Hth :)

 

[TomHart]

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?

 

[haruspex]

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.

 

[ooohffff]

Do you know the answer to this problem? If so, can you post it?

No, I do not know the answer.

 

[haruspex]

Homework Equations

Any conservation laws that might apply?

 

[ooohffff]

Any conservation laws that might apply?

Conservation of angular momentum?

 

[haruspex]

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?