LESSON 4: Moments 2
Let’s continue to analyze moments by clarifying what we mean by “perpendicular distance”. The perpendicular
distance from a point to a vector is not the actual distance between the point and the vector, it is the
distance in either the x-direction or y-direction. If the vector’s direction is along the y-axis, then the
perpendicular distance is the distance separating the point and end of the vector in the x-direction. The
vice versa is also true (if vector is in x-direction then distance is in y-direction).
As you can see from the diagram, the vector is actually located 5 meters from the point, but the
perpendicular distance, which is in this case the distance in the y-direction, is only 4 meters.
Let’s do a slightly more complicated example involving angled vectors.
In this example (to the left) we will find the unknown magnitude of the green vector. We will use the variable “?” to
indicate the magnitude of the green vector. To begin, we should break the green vector into its component
parts.
This vector is the same as two vectors, one along the y-axis with a value of ?sin(60) and the other
along the x-axis with a value of ?cos(60). Since this vector along the x-axis of value ?cos(60) is in line
with the pin joint, it will not create a moment about the pin.
Simply put, this vector will not cause the
bar to spin about the pin joint. The red vector will create a moment of 40 Nm (10x4) in the counterclockwise
direction, so the y component of the green vector must cause a moment of 40 Nm in the clockwise direction.
The perpendicular distance from the pin joint to the y-component of the green vector is 3 meters, so by solving
the formula: 3 * ?sin(60) = 40 we can find the magnitude of the green vector. ? = 15.396 N
(note: if you summed the forces in the x-direction or y-direction and found that this problem did not follow
the laws of statics, that was because there are actually two unlabeled vectors that the pin joint exerts on
the bar. I did not label these vectors because they are in line with the pin joint, and therefore do not create
a moment about the pin joint (they don’t cause the bar to spin). )