Constraint of moment about an axis

[goldfish9776]

Homework Statement

why there is no constraint of plate about a axis ?
for moment about z -axis , i can have -2Bx +3By = 0 , where By and Bx = 0 which is shown in the top part of solution...

Homework Equations

The Attempt at a Solution

 

[haruspex]

I don't understand your question. None of the forces acting on the plate have a moment about the z axis through B.
If you take moments about the z axis through other points, Bx and By could have moment, but as demonstrated both those forces are zero.
Can you clarify your question?

 

[goldfish9776]

I don't understand your question. None of the forces acting on the plate have a moment about the z axis through B.
If you take moments about the z axis through other points, Bx and By could have moment, but as demonstrated both those forces are zero.
Can you clarify your question?

an why there is no restriction about moment about Z ? i think there is also restriction of moment about Z because i can form the equation -2Bx +3By = 0 , so it can prevent the object from rotating about the z axis ...

 

[haruspex]

an why there is no restriction about moment about Z ? i think there is also restriction of moment about Z because i can form the equation -2Bx +3By = 0 , so it can prevent the object from rotating about the z axis ...

Sure, but it doesn't tell you anything extra. Bx and By are both known to be zero, so that reduces to 0=0.

 

[goldfish9776]

Sure, but it doesn't tell you anything extra. Bx and By are both known to be zero, so that reduces to 0=0.

So, if there is the moment restriction about an axis, the force which causes the moment must be non zero value? I.e. There must be at least a counterclockwise and clockwise moment to prevent rotation, so that it can restrict the moment about an axis?

 

[haruspex]

So, if there is the moment restriction about an axis, the force which causes the moment must be non zero value? I.e. There must be at least a counterclockwise and clockwise moment to prevent rotation, so that it can restrict the moment about an axis?

I'm not sure what you mean by a moment 'restriction'. Do you mean some physical connection which prevents rotation? Or do you mean a sum of forces law? In a static arrangement, the moments must balance. That can be achieved just as well by there being no nonzero moments as by there being nonzero moments which cancel.

 

[goldfish9776]

I'm not sure what you mean by a moment 'restriction'. Do you mean some physical connection which prevents rotation? Or do you mean a sum of forces law? In a static arrangement, the moments must balance. That can be achieved just as well by there being no nonzero moments as by there being nonzero moments which cancel.

As we can see in the question , for moment about x and y =0 , the moment is restricted about x and y axis... Why not the moment is restricted about the z axis? Since we can form the equation
-2BX +3BY=0

 

[haruspex]

As we can see in the question , for moment about x and y =0 , the moment is restricted about x and y axis... Why not the moment is restricted about the z axis? Since we can form the equation
-2BX +3BY=0

As the text says, if you were to add a force, no matter how small, that had a moment about the z axis through B then the plate would turn. There is no other force that has moment about that axis, so there would be nothing to oppose the additional force.
The Bx and By forces would not have a moment about that axis even if those forces were nonzero.

 

[goldfish9776]

As the text says, if you were to add a force, no matter how small, that had a moment about the z axis through B then the plate would turn. There is no other force that has moment about that axis, so there would be nothing to oppose the additional force.
The Bx and By forces would not have a moment about that axis even if those forces were nonzero.

why ? they have some distance (r) from the z axis , right ?

 

[haruspex]

why ? they have some distance (r) from the z axis , right ?

When you say "z axis", you mean the axis in the z direction that passes through point B, right? How can a force that also passes through that axis be at a nonzero distance from it?

 

[goldfish9776]

When you say "z axis", you mean the axis in the z direction that passes through point B, right? How can a force that also passes through that axis be at a nonzero distance from it?

no , i mean z a-xis , not Bz axis

 

[haruspex]

no , i mean z a-xis , not Bz axis

Ah, ok.
I think the author meant the z' axis, i.e. the vertical axis through B. But she might have been using "rotation about the z axis" in a generic sense, i.e. any rotation in the xy plane.

 

[goldfish9776]

Ah, ok.
I think the author meant the z' axis, i.e. the vertical axis through B. But she might have been using "rotation about the z axis" in a generic sense, i.e. any rotation in the xy plane.

if the plane can't rotate in Bz axis , it can't rotate as well as in z -axis?

 

[haruspex]

if the plane can't rotate in Bz axis , it can't rotate as well as in z -axis?

I think the author means that if there were a torque added perpendicular to the XY plane then there would be a rotation in that plane. This is true, and specifically, it would be a rotation about the z' (i.e. Bz) axis. It cannot rotate about any other z-direction axis because of the ball-and-socket joint at B.