Is the net torque calculated correctly in both pictures?

[davon806]

Homework Statement

Please see the attached,both picture shows the weight acts on the centre of mass.
In picture 1,the net torque acts on the object about the pivot is Wcosθx
In picture 2,I resolve the weight into two components.Wcosθ and Wsinθ,
the net torque about the pivot is Wcosθx - Wsinθy

Which one is correct?Thx

Homework Equations

The Attempt at a Solution

As mentioned above and the attached

 

[mfb]

How do you get the first expression?
It cannot be right: If the center of mass would be right above the pivot (=> 0 torque), you would get the same torque with that formula.

 

[davon806]

No,I assume that the centre of mass is at the left of the line of pivot.
Or let's think in this way,
the weight is the only force that causes the object to rotate about the pivot,
the perpendicular distance between the centre of mass and the pivot = xcos(theta) m
So the moment about the pivot = Wxcos(theta) Nm
But if we resolve weight into horizontal and vertical components,
clockwise resultant moment = Wsin(theta)y
anticlockwise resultant moment = Wcos(theta)x
So the resultant moment about pivot = Wcos(theta)x - Wsin(theta)y ?

 

[mfb]

No,I assume that the centre of mass is at the left of the line of pivot.

I don't see how this assumption is used to get Wcos(θ)x.

the perpendicular distance between the centre of mass and the pivot = xcos(theta) m

No.

 

[davon806]

Why?
What is the formula of the resultant moment about the pivot?

 

[davon806]

push

 

[mfb]

Wait, you changed the definition of x there. That is possible (and gives the correct result), but then you cannot compare it to the other way to calculate it.

push

That does not help, I cannot answer when I am not here anyway :p.

 

[davon806]

Sorry for my ugly drawings and thanks for your reply :)
But if picture 1 is correct,i.e.
the net torque acts on the object about the pivot is Wcosθx
Then picture 2 is incorrect,
anticlockwise moment=Wcosθx
clockwise moment=Wsinθy
As the object would rotate anticlockwisely,
Wcosθx > Wsinθy,so the net moment about the pivot = Wcosθx - Wsinθy?

 

[mfb]

Wcos(θ)x - Wsin(θ)y is right with your first definition of x and y, Wcos(θ)x is right with your second definition of x. As you can see, it is a bad idea to use two different definitions for the same variable at the same time.

 

[davon806]

Thank you very much.:)
I finally realize why I would make such a silly mistake.It's simply due to my ugly drawings.