Torque and Center of Gravity in Rotating Objects

[v54]

Hi !

2 Objects turn at constant rotational velocity ω rd/s around axis noted "axis" on image (ω clockwise). An external system not drawn force the study to turn at ω rd/s if necessary. From blue object, forces F1 and F2 are applied to orange object. F1 = -F2 in vector.

I would like to know if orange object receive a torque and turn around its center of gravity "cg2" if I apply F1 and F2 forces ? I think if I want to apply a torque on orange object linear velocity must be the same of two points "A" and "B" where forces are applied. It's possible for a small distance dx I think. If I add a rotational velocity anticlockwise to orange object, it's possible to have the same velocity for each point. In this case F1/F2 forces on orange object will decrease potential energy, but this energy can be recover, no ?

Blue object receive a torque F2*d2-F1*d1 in the direction of rotation, so how the orange object cancel this torque ?

Thanks a lot for your reply !

 

[CWatters]

Lets call the axis point O.

You have drawn F1 orthogonal (at right angles) to the line OA (marked D1 in your drawing) but why isn't F2 orthogonal to OB?

 

[v54]

I take F1 = - F2 in vector for have a torque to orange object. I place F1 and I have no choice for F2.

I think I need to take ω = -ω' like that velocity of each point of orange object is the same everywhere.

 

[v54]

If blue object turn at ω and orange object turn at -ω it's like object orange move in translation ?

I drawn first image for look at details of forces and second for look at different positions in time. The green point of orange object don't turn for me, can I say orange object move in translation ?

 

[v54]

In the last message, I'm wrong, orange object don't move in translation.

I simulated 2 rotations, with rotational velocity ω for blue object and -ω for orange object, I can see objects are turning from an external viewer (+ω and -ω). So, if I apply a torque on orange object I need energy, this energy goes to kinetics energy of rotation for orange object. Now, the blue object receive the same torque but in the other direction and increase its rotational velocity. Like this torque increase kinetics energy of rotation (blue object) I think I need to give this energy but how ?

 

[CWatters]

I'm not quite sure where you are going with this.

Is there friction between the blue and orange objects?

If yes, then the orange object will eventually rotate with the same angular velocity as the blue box it's in.

If no, then the orange object will retain it's original orientation.

 

[v54]

Just understand combination of rotational velocities and torques. No friction. If I apply a torque on orange object from blue object, this torque is apply to blue object in other direction, no ?

 

[CWatters]

How does the blue object apply a torque on the orange object if there is no friction between the two?

If there is no friction...When the blue object rotates the orange object will not rotate. It's inertia will keep it orientated in the same direction. I believe this diagram is correct..

 

[v54]

Thanks for the diagram.

How does the blue object apply a torque on the orange object if there is no friction between the two?

I added a motor for example between orange/blue objects. If rotational velocity of orange object is -ω and ω for blue object. The rotor fixed to the orange object give a torque to it, so the motor increase the rotational velocity of orange object, and this need energy, I'm ok with that. Now, the stator is fixed to the blue object, a torque is applied to blue object and this need energy too. Forces from stator to blue object exist because they are forces on rotor (reaction), it's not forces alone. If I give forces alone, sure they need energy but here how the stator consume more energy because it turns around blue object ?

 

[CWatters]

I'm lost. You mention a "stator" (normally a stationary object) turning around the blue object.

I'll let someone with more time try and work out what your question is.