Study Blog Part 2: System of Forces

i) Topics covered

1) Forces

2) Torque

3) System of forces

ii) Time spent/what sessions?

1/2 Lecture (1H)

Self-Study

2 Problem Solving Sessions (on my own) (2.5 x 2 H)

Repetition (~2 H)

Amount of hours: 8 H

I did as I had planned; studied more on my own time. I did most of the weekly exercises, so I am quite content in that regard. I arrive late to the lecture (missed the first part of the lecture) and skipped the second one (did it on my own).

It was more to this week than what I thought it would be, but it was still an alright amount. Just beneath the amount where it becomes challenging to get it all done! I did put in more effort than last week, so maybe that is also a factor to why it felt a it easier to get it all done.



iii) Topics explained


We are still working through fundamentals of the course, but that doesn't mean it isn't interesting! It's rewarding to feel confident in my vector algebra and to see and use vectors in different ways. I think I am developing a greater view of how to connect concepts in mechanics (sounds a bit too ominous to say while only being in the second week of the course....)

Topics of the week

1) Forces

2) Torque

3) System of forces



We didn't really discuss much about forces as a physical concept, but moved on pretty quickly as to define it in a vector space and make calculations on forces. We did define forces as to have three properties; a magnitude, a direction and a point of action. Basically, they are a fixed vector. A force is either a push or a pull.

Interesting, from a more philosophical point of view is that forces always act between two bodies. Nowhere to be found is an example where an isolated frame of reference containing only one body has a resultant force acting upon it. Might not come in handy in very many situations, but still, it's an interesting idea to keep in mind.

A torque is a measurement of rotation around a point or axis, also called a moment. The moment is directly related to the distance from the point/axis of rotation to the force component, acting in the orthogonal (perpendicular) direction to the distance. In 3D calculations, the moment around a point can be found by the cross product rule; Mo=r x F (bolded letters are vectors!).

The observant mind would recognize that the cross product between two vectors is in fact a vector in itself. The moment around a point (in 3D; in 2D, the moment acts around the third axis!) is a vector. What is then the physical meaning of this vector? A moment is a rotation, and a rotation isn't very likely to be explained by an arrow in space, e.g. a vector.

The answer to this question is that the moment vector is the vector that the rotation occurs around, i.e. the vector can be seen as the rotation axis, in which the rotation occurs around. The magnitude of the rotation is proportional to the length of the vector, or the magnitude of it. The direction of the rotation (which direction are we rotating around; clock-wise or counter clock-wise around the axis?) is determined by the direction of the vector and the Right Hand Rule.

The Right Hand Rule can be explained as following: Using your right hand, form a fist. Then, stretch out your thumb so that it is point out from the clenched fingers forming the fist. Now, loosen up the fist. Using your thumb, point into the same direction as the vector. Your other fingers will be formed as a semi-circle and hence point in the direction of rotation. It is very important that you use your right hand; using your left hand will result in pointing towards the opposite direction!


Before moving on to talking about system of forces, we have to define what a couple is: A force couple are a system of forces (usually only two!) which have no resultant force acting on the system. However, due to the forces being a distance apart, a moment will occus. A better term would be pure moment.

When dealing with system of forces, the common goal is to reduce the system a simplified system. The goal is to reduce all of the forces to one resultant force and to have only one moment. To do this, we take advantage of the concept of equimomental systems: two systems are said to be equimomental if the resultat force and moment are the same in both systems.

Therefore, moments and forces would have to be moved in systems. Using the concept of couple forces, we can motivate how to move forces. Let's say we have a force F which is acting upon the point A. Now, we wish to move F to the point B (we are still working in a equimomental system to the first one!); we add the force F and -F at point B (adding no resultant force or moment to the system). Couple forces say that F acting at A and -F acting at B cancel out and are replaced by a moment (concept of couple forces) which act upon point B. Now, we still have an equimomental system to the first, but now F is acting upon B with the accompanied moment.

To see how the moment is in another point relates to original point, the following relation can be use:

Mb=Ma + r x F
where a and b are point and r is the distance from the point b to a.

Usually, a system can only be reduced to a force and a moment (or two forces acting as couple forces), but sometimes, systems can be reduced to one single force resultant. The criteria for this is that the dot product between the resultant force F and the moment Mo has to be zero. If the criteria is met, the point can be found with the help of the formula above (Mb=Ma + r x F) by setting r to point towards the unknown point.

I didn't get around to doing any exercises, the reason being is that I didn't start doing exercises to print during the week, and redoing exercises to print just before printing the blog takes too much time...

Hopefully, some will come next week!

How does the moment become altered if the force is moved in the direction of its action?

How would you calculate the moment around an axis in a space? (It can be done in two steps!)

Define what is meant by two equimomental systems

Define what is meant by coupled forces

List the three properties related to forces

i) What topics? What do you know about this?

1) Center of mass

2) Equilibrium

Center of mass, I think, will be about finding the center in geometrical objects. Instead of always the center is given, the center will have to be calculated and/or found.

Equilibrium is the center concept in Statics. It will be what we have done previously, but combined into one. Equilibrium is basically about simplifying complex force systems into a summarized equimomental system.

Equilibrium is a large potion of this mechanics course, so it will be covered in the week after the next one as well.

ii) Goals?

We have some problems that are to be handed in and graded. I should get started with that next week. Could be a nice repetition of this week and last week!

I'll skim through the next chapters in the book. Maybe I can skip one or two of this week's lectures as well?

Also, when doing exercises, aim to do some on scannable paper so that I can upload them here ^^