This is an illustration of the moment of a force, [math]\vec{F}[/math], applied at a position, [math]\vec{r}[/math] about the origin in two-dimensions. You can move the two blue points to change the force and position. Note: move the position first. A moment may also be called a Torque.

[list][*]Move the position and force around and note how the Moment changes[/*][/list]When is the moment positive and when is it negative? How might the change in sign be related to your right hand?[br][br][list][*]Check Parallel Line[/*][/list]This will draw a line parallel to [math]\vec{r}[/math] through a point you can move. Move the force so that it ends on the parallel line. Note the size of the moment shown. Then move the force along the parallel line.[br]How does the moment change?[br]Hint: Putting the [math]\vec{r}[/math] vector to snap to a grid line and the parallel line point to snap to a grid line will allow you to snap the Force to be exactly on the parallel line.[br][br][list][*]Check Angle[/*][/list]This will show the angle between the force and the position vector and the way to calculate the moment from the magnitudes of the position and force vectors and the angle between them. Calculate a few moments using the values shown.[br][br][list][*]Check Force Projection[/*][/list]This will show components of the force in the direction of [math]\vec{r}[/math] , [math]F_r[/math], and perpendicular to the direction or [math]\vec{r}[/math], [math]F_p[/math]. The method for calculating the moment from the magnitudes of the position and perpendicular force component is also shown. The sign of the result still needs to be determined, how would you determine the sign of the moment?[br][br][list][*]Check Parallelogram[/*][/list]This will show the area of the parallelogram made with sides parallel to the position and force vectors. How does this area compare to the moment? How would you determine the magnitude and sign of the moment from the area of the parallelogram?[br][br][list][*]Check Components[/*][/list]This will decompose the position and force vectors into components parallel to the axes and show the formula for calculating the moment from the components. A slider allows you to slide the force components along their line-of-action to the position components tips. What would be the moment of each pair of components?[br][br][list][*]Check Component Projection[/*][/list]This shows the vector projection of the Force vector in the direction of the position vector, [math]\vec{r}[/math] . The formula shown comes from the dot product, [math]\vec{a}\cdot\vec{b}=\left|a\right|\left|b\right|\cos\theta[/math] , and the projection magnitude is the vector magnitude times the cosine of the angle between vector, [math]\text{Magnitude of }\vec{a}\text{ projected on to }\vec{b}=\left|a\right|\cos\theta[/math]. How might you use this dot product to find the angle [math]\theta[/math] ?[br]