Will the real TeeEm please stand up!

number theory is pure maths and I do not do pure maths ...
On a serious note I have an amazing book on number theory, but the problem is that is not in English.

Ah, not to worry, the book Physicsmaths recommended looks great

Ah, not to worry, the book Physicsmaths recommended looks great

maybe I also have the title?

Art of problem solving is one of the best sites out there. Wonderful.


Posted from TSR Mobile

Art of Problem Solving Intro to Number Theory. I think the only UK stockist of AoPS books is UKMT here. It is quite expensive but looks like the kind of book you keep forever.
.

Art of Problem Solving Intro to Number Theory. I think the only UK stockist of AoPS books is UKMT here. It is quite expensive but looks like the kind of book you keep forever.


I have had a look at there books in the past, they do look brilliant. Just trying to decide what maths I want to spend time ding; STEP 1 prep or some number theory/olympiad type problems.

Most people who do well in olympids do well in step.


Posted from TSR Mobile

x

I dont suppose you have any questions on moments acting on a lamina? I did flip through your moments booklet but they were mainly M1 type problems. Had a very hard question today from the old M2 book.

I dont suppose you have any questions on moments acting on a lamina? I did flip through your moments booklet but they were mainly M1 type problems. Had a very hard question today from the old M2 book.

Is it the part after finding the centre of mass that is giving you grief? What sort of a question was it, hanging it up, balancing it on a slope (I've always thought that this wouldn't work in practice) or attaching a stud and then hanging it up?

these are very rare and not too hard
there may be parts of questions of what you are describing with centre of mass workbooks in M2 and in M3

Ok will have a quick look 👍

There was a rectangular lamina lent up against a wall. It was basically a ladder problem with rough ground but the ladder was a rectangular lamina. The difficulty lies in the line of action of its weight because it came down from the CoM of the rectangle.

There was a rectangular lamina lent up against a wall. It was basically a ladder problem with rough ground but the ladder was a rectangular lamina. The difficulty lies in the line of action of its weight because it came down from the CoM of the rectangle.

Like question 9 here?

I will make a question like that...
I remember in the early nineties a question with a wardrobe leaning against a wall

I seem to have every old Mechanics book except that one.

Attached is a diagram of what I think you've got. I've put on 4 forces, the weight of the lamina, the reactions at the wall and the ground and the friction at the ground.

I'm guessing that what is giving you grief is finding a suitable distance when taking moments for the weight. If you take moments about A, the distance you need is the distance from the centre of mass to the wall, GB. This is a side of the triangle that I have drawn, with hypotenuse AG. The angle between AG and the wall is alpha + beta. Alpha is the angle between the side of the lamina and the vertical, which I guess is what you are trying to find. beta depends on the dimensions of the rectangle.

Does that help at all?

Like question 9 here?

Another question came up in M2 today. It was Q29 of Review Exercise 2 in the old edexcel book, the 2000 one. The issue was dealing with the moments about O and how to deal with the centre of mass acting from the 'centre' of the rectangular lamina.