Chapter 2 Review of Forces and Moments - Brown University

2.3.2 Pure moments, couples and torques.- Definition, Physical Interpretation, and Examples
A pure moment is a rotational force. Its effect is to induce rotation, without translation – just like a force
couple.
Couples and torques are other names for a pure moment.
A pure moment is a vector quantity – it has magnitude and direction. The physical
significance of the magnitude and direction of a pure moment are completely
equivalent to the moment associated with a force couple system. The direction of a
moment indicates the axis associated with its rotational force (following the right
hand screw convention); the magnitude represents the intensity of the force. A
moment is often denoted by the symbols shown in the figure.
A 3D moment
A 2D moment
The concept of a pure moment takes some getting used to. Its
physical effect can be visualized by thinking about our beambalancing
problem again.
W
d
k
j
i
The picture above shows the un-balanced beam. We saw earlier that we can balance the beam again by
adding a second force, which induces a moment equal and opposite to that of the force W.
We can also balance the beam by applying a pure moment to it. Since the moment of W is dWk , a
moment M =−dWk applied anywhere on the beam would balance it.
d
d
M= - dWk
W
W
j
d
M= - dWk M= - dWk
d k i
W
W
You could even apply the moment to the left of the beam – even right on top of the force W if you like!
2.3.3 Units and typical magnitudes of moments
In the SI system, moments have units of Nm (Newton-meters).
In the US system, moments have units of ft-lb (foot pounds)
The conversion factor is 1 Nm = 0.738 ft lb; or 1 ft-lb = 1.356 Nm.
Typical magnitudes are:
• Max torque exerted by a small Lego motor: 0.1 Nm
• Typical torque output of a typical car engine 300-600 Nm
• Breaking torque of a human femur: 140Nm