Moments Problem Regarding Sign Convention?

[-overrated]

Homework Statement

The handle of the hammer is subjected to the force
of F = 20. Determine the moment of this force about the
point A.
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Homework Equations

Principle of moments: Mo = FxY - FyX

The Attempt at a Solution

I have broken the force into x and y forces
and using the Principle of moments: Mo = FxY - FyX
I have gotten 20cos30(18)-20sin30(5) however in the solution manual the answer is -20cos30(18)-20sin30(5). How do I know where to put what signs in these kind of equations. I know that positive is CCW and negative is CW but when broken into components how do you know what signs to use?!

 

[PhanthomJay]

Use the right hand rule for each component of force. Both components produce clockwise moments about A, hence , both moments are negative using the convention you have chosen. Forget about the minus sign in your relevant equation. You decide whether plus or minus.

 

[-overrated]

I wasn't really able to grasp the idea of the right hand rule. My professor is always just waving her hands around and didn't explain it well enough, can you explain to me quickly how I would use the right hand rule?

 

[PhanthomJay]

Yeah, you've got to waive your right hand around a lot to properly twist it in the correct orientation, sometimes nearly straining your wrist, which is the case here when determining the sign of the sin component of the force. It takes some practice. The cos comp of the force acts up and rightward, the sin comp acts up and leftward.

You will find several definitions of the right hand rule. With your 4 fingers of your right hand extended and the thumb extended perpendicular to the fingers, place your fingers pointing in the direction of the force component along the line of action of that force component , and then curl your fingers toward the point you are taking moments about. In so doing, if your thumb points inward toward you, the moment is ccw; if it points outward away from you, the moment is cw. If you can't curl your fingers toward the pivot point, flip your wrist 180 degrees. Don't sprain it.

 

[-overrated]

Aha, thanks Jay! I think I got the hang of it, but yeah definitely it does hurt your wrist. I did catch my thumb slightly pointing towards me which is a good sign because they were both clockwise.

 

[PhanthomJay]

You mean pointing away from you, no?

 

[-overrated]

Darnit, on second thought maybe I do not have it then. My fingers are pointing up to the right regarding the cosine and I curl my fingers towards point A my thumb sort of goes to the left I am not sure if I can say if its outwards or inwards.

 

[PhanthomJay]

Once you point your fingers in the direction of the line of action of the force component and curl them toward the pivot point, your thumb is pointing into the plane of the computer screen, into the 3rd dimension or z axis. That's what i meant by away from you.

 

[-overrated]

Yes, now I do think I have it straight, sometimes the direction at which my thumb points can be a bit ambiguous.

 

[PhanthomJay]

Yes, it can be ambiguous. But when looking into the third 'z axis' dimension , the words 'left' and 'right' lack meaning.