Finding the Torque on a Fixed Square

[JClay813]

Homework Statement

Hello,

I'm having trouble with the following problem. I am given a square of length L and mass M that is fixed at its center. A rod of length l is is attached to the top left corner of the square, with a mass m attached on the other end. A motor applies a torque on the rod, this torque has magnitude t₀ e^iwt. Where t₀ is a drive torsion. I need to find theta₁, and theta₂.
theta₁ denotes the angle between the rod and the square, while theta₂ denotes the angle of rotation.

I have attached an image for some more clarity.

Thank you

Homework Equations

The Attempt at a Solution

I know that torque is given by F x r, but I'm not seeing how that helps me find either of the angles[/B]

 

[tnich]

Homework Statement

Hello,

I'm having trouble with the following problem. I am given a square of length L and mass M that is fixed at its center. A rod of length l is is attached to the top left corner of the square, with a mass m attached on the other end. A motor applies a torque on the rod, this torque has magnitude t₀ e^iwt. Where t₀ is a drive torsion. I need to find theta₁, and theta₂.
theta₁ denotes the angle between the rod and the square, while theta₂ denotes the angle of rotation.

I have attached an image for some more clarity.

Thank you

Homework Equations

The Attempt at a Solution

I know that torque is given by F x r, but I'm not seeing how that helps me find either of the angles[/B]

I am glad to see that you have drawn a diagram. That always helps in solving problems like this. Looking at the diagram, I have some questions:
1) Where is the motor?
2) In which direction (cw or ccw) does the torque act?
3) Your torque magnitude is a function of time and is a complex variable. In general a magnitude is a real number. What does it mean to have a complex torque magnitude?
4) Are you intending to find the angles as functions of time?
5) The rod is attached to the square at the upper left hand corner. This could not be an equilibrium position because the mass at the end of the rod would tend to rotate the square ccw. So at what time is the square oriented with the rod at the upper left hand corner?

 

[JClay813]

I am glad to see that you have drawn a diagram. That always helps in solving problems like this. Looking at the diagram, I have some questions:
1) Where is the motor?
2) In which direction (cw or ccw) does the torque act?
3) Your torque magnitude is a function of time and is a complex variable. In general a magnitude is a real number. What does it mean to have a complex torque magnitude?
4) Are you intending to find the angles as functions of time?
5) The rod is attached to the square at the upper left hand corner. This could not be an equilibrium position because the mass at the end of the rod would tend to rotate the square ccw. So at what time is the square oriented with the rod at the upper left hand corner?

The motor is on the upper left corner of the square, oscillating the rod. This is all of the information I have, so I'm not sure what to do.

 

[CWatters]

Perhaps it's just me but..

How can anything move if the motor is top left and the square is "fixed" in the middle?

Can you add the motor and its axis of rotation to the drawing?

 

[JClay813]

The square is fixed in the middle so that it can rotate around the center. The "motor" oscillates the mass on the rod up and down, parallel to the sides of the square.

 

[CWatters]

If the square, rod and mass are all attached (fixed together rigidly) they can only rotate about the centre of the square. In that case the mass cannot move linearly "up and down". If the mass is free to slide on the rod it could move linearly up and down. Is that the case?

 

[JClay813]

If the square, rod and mass are all attached (fixed together rigidly) they can only rotate about the centre of the square. In that case the mass cannot move linearly "up and down". If the mass is free to slide on the rod it could move linearly up and down. Is that the case?

No, the mass is fixed on the end of the rod

 

[haruspex]

The square is fixed in the middle so that it can rotate around the center. The "motor" oscillates the mass on the rod up and down, parallel to the sides of the square.

Am I right in thinking that the motor is what connects the rod to the square? I.e, the motor is mounted on the square and flaps the rod back and forth, like a shoulder muscle flapping an arm.
I assume gravity is to be ignored, e,g. this is in a horizontal plane.

Draw separate FBDs for the arm and the square. Consider what forces act at their junction.