M1 vector / moments question

hi, I would like some help on this question pls. I am have clue how to go about doing this as this also involves vectors. I saw in other threads that it involves working out the angle in between. But I thought moments just involves force * mass and the direction of it? A diagram will really help as I can't really picture it. Thanks.

Here's a rough diagram - you can draw something more accurate than me.



The moment of a force is the force multiplied by the perpendicular distance to the pivot.

This perpendicular distance is shown as the dotted line in my diagram.

Hi, I don't get why the dotted line is drawn like that in that particular direction...

It's the perpendicular distance from the line of action of the force to the origin.

If I extend the line of action of the force then it may be clearer where the perpendicular distance is:



The line shown here is the same length as the dotten line before.

With the line drawn, what do I work out then? The angle in between? Also how to u know which direction the force will turn to. Clockwise or anti clockwise?? Thanks.

This is this actually quite a hard question for M1. Is it really an M1 question? - it wouldn't come up in any M1 exam. The question is easier if you use the scalar product but that doesn't come up until A2.

The moment of the force F₁ about the origin O is the magnitute of F₁ multiplied by the perpendicular distance from the line of action of F₁ to O.

Below I've added some values to my diagram using the vectors given in the question. 'd' is the perpendicular distance that you need to find.



See if you can use trig to find the value of 'd'. Then multiply this by the magnitude of F₁ and you're done. Let me know if you need more help.

I get the answer as 16Nm if you want to check it.

For the sense of the moment, imagine this is a see-saw question where O is the centre of some rod and there's a force F₁ applied from the point A on the rod. Is this an anitclockwise or clockwise moment about O?

This is from the m1 solomon paper. So i just need to work out what d is ? And i think the direction is anticlockwise? I am not very sure ...

You just need 'd' and then multiply it by the magnitude of the force.