Statics

Lesson 02

Moment -- or, a tendency to rotate

🟦  2.1  Introduction to moment (of a force)

❏ Moment (of a force)

A moment (of a force) can be thought of as a tendency to rotate about an axis.

A force is a tendency to translate; a moment is a tendency to rotate.

We compute a moment by multiplying a force by a distance. Therefore, moment has units of force times distance. 

Inspect this flipbook for an introduction to the concept of moment.

In terms of notation, we use the symbol M for moment. 

Graphically, we convey moment with a curly arrow (↺ or ↻).

❏ Flipbook: An introduction to moment

❏ The equation for moment (of a force)

The simplest scalar expression for moment is M = Fd. 

Verbally, we'd say "the moment about an axis is equal to a force multiplied by its perpendicular distance to that axis."

In 3D, an axis is a line (or really, a ray). In a 2D projection, an axis is a point, because the axis is perpendicular to your screen or paper. 

To properly visualize the moment, you must draw the 2D plane that is normal (perpendicular) to the axis of rotation.

We can use a subscript after the M to indicate the axis of rotation being studied. We can pick any point that lies on the axis of rotation and call it Point A. Therefore, we can write MA if we wish to indicate the moment about Point A.

We will learn the vector formulation for moment (M = r x F) in Lesson 14.

❏ Moment about an axis (3D)

In a 3D drawing, we can dash in the axis of rotation. In 3D, it is a line (or ray).

❏ Moment about a point (2D)

In a 2D drawing, we orient the drawing so that the axis is perpendicular to the plane of the screen or paper. Now, the axis of rotation appears as a point.

🟦  2.2  Rotational motion vs. a tendency to rotate

I use the analogy of a pushpin to introduce the topic of moment.

THIS IS GOING TO BE THE NEW SKETCHUP SINGLE PUSHPIN MODEL

🟦  2.2  Scope and organization of this lesson

In the next few sections, we'll learn about a series of concepts that are easily confused by Statics:

There are specific rules that dictate when you must include or exclude the curly arrow from your diagram. These are explained below in section ____.

❏ Moment vs. torque

The idea that engineers call a moment is called a torque by physicists.

Engineers also use the word torque, but for us, it means something slightly different. For engineers, a torque is the sub-type of moment that tends to twist solid material. This concept is not studied in Statics.

For the purpose of learning Statics, we use the term moment exclusively for what was (likely) called torque in your Physics course.

🟦  2.3  How to calculate a moment

❏ Subtitle

Imagine that you have a small yellow piece of paper and a desk made of a corkboard. 

You push a green pushpin located somewhere in the upper right quadrant of the yellow paper.

Your goal is to make the the yellow post-it note rotate counterclockwise (CCW). To that end, you'll need to induce a moment abut the z-axis of the pushpin.

You can't have a moment without a force, so you enlist a friend to apply a push force in the negative y direction with a pencil, as shown.

You are able to calculate the magnitude of the moment by using the simple equation M = Fd. 

In this equation, F is a magnitude (neither positive nor negative), and d is a magnitude (neither positive nor negative).

We also need to establish a sign convention for moment:

Since F and d are both magnitudes, we determine the sign of M by inspection by visualizing the tendency to rotate.

❏ A moment about z

❏ The sign convention for moments

❏ Mastering the sign convention for moments: CW vs. CCW

For example, consider the five examples below. Each is a mini-flipbook containing two images. Determine whether or not the moment about pushpin A is positive or negative. Check your work on each problem; work these as many times as needed to master this important concept.

❏ Mastering the sign convention for moments: thumbs up vs. thumbs down

Another way to work through signs of moments is to use your right hand. You curl the fingers of your right hand in the direction of the tendency to rotate. When you're making a "thumbs up" gesture, the moment is positive. "Thumbs down" is a negative moment. Practice this approach in the five mini flip-books below. Each mini flipbook has two slides.

Do 5 more mini-flipbooks below. Here, keep the same force, but put the pushpins in 5 different locations.

🟦  2.x  Visualizing the rotation of a body about an axis

don't forget about the blue rod supporting the yellow object held by a hand. Do that for a moment summation equation.

x pushpin analogy (or, using your left hand to hold a pen, which is the axis, and your right hand to figure out the sign)

🟦  2.x  Translational Motion + Rotational Motion = MOTION

In order for some sign convention shortcuts to work, it's best to have the positive direction of the axis of rotation come out of the screen (or paper) towards you.


❏ x

x

❏ Flipbook: x!)

x

x

🟦  2.x  Moment as lever (types of levers)

Class 1: seesaw or pliers

Class 2: nutcracker

Class 3: tweezers

❏ Animation: Types of Levers

x

🟦  2.x  When to include / exclude the curly arrow for moment in a drawing

x


🟦  2.x  Force couples (and explain why I always put "forces (and moments)" as a parenthetical note)

Varignon's theorem

x

➜ Practice Problems

coming soon

seesaws? lots of them?