1.2 Nanoscale Actors and Their Properties

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Figure 1.17: a) Torque = F•r⊥. r⊥is the perpendicular distance from the pivot point to the lever arm, the

line of force. Torque is the rotational analogue of force. b) If you make the force perpendicular to the ra-

dius, you maximize r⊥and thus maximize torque. Your force will be most effective in this case. By increas-

ing the length of the lever, your force also becomes more effective.

Figure 1.18: Elasticity. a) The ball is fully elastic. The energy of impact was converted into usable energy

that carried the ball back up to the height it started from. b) The ball is partially elastic. Some of the energy

was usable and it carried the ball back up part of the way, but not to the starting point. The rest of the en-

ergy was converted into the deformation of the ball and heat. c) The ball is completely inelastic. All energy

of the impact was converted into deformation and heat.

Let us look at the strength of a material in more detail. There are different stresses or

forces acting on a material: tensile stress (stretching the material), pressure (pressing

on the material – let’s start with hydrostatic pressure that equally comes from all sides),

and shear stress that comes to the sample from the side (Figure 1.19). In all cases, the

force results in strain, which is a change in dimensions proportional to the stress or

force. For tensile stress, the sample elongates in one direction, for pressure it becomes

shorter in three directions, and for shear stress the top of the sample elongates more

than the bottom.

Generally, the strength of the material is characterized by the modulus. This de-

pends on the type of modulus that is measured (it is usually the tensile modulus, or

Young’s modulus, E). Note that it is strength that we discuss here, not toughness; we will

discuss toughness a little later. All of these moduli assume that the material is ideal, i. e.,

that if the force/strain is removed, the material will go back to its original state instantly.

For most materials, this is only true when small stresses are applied. Real materials with