Chapter 13

### INTRODUCTION

After completing this chapter, you will be able to:

• Define torque, quantify resultant torques, and identify the factors that affect resultant joint torques.

• Identify the mechanical advantages associated with the different classes of levers and explain the concept of leverage within the human body.

• Solve basic quantitative problems using the equations of static equilibrium.

• Define center of gravity and explain the significance of center of gravity location in the human body.

• Explain how mechanical factors affect a body's stability.

Why do long jumpers and high jumpers lower their centers of gravity before takeoff? What mechanical factors enable a wheelchair to remain stationary on a graded ramp or a sumo wrestler to resist the attack of his opponent? A body's mechanical stability is based on its resistance to both linear and angular motion. This chapter introduces the kinetics of angular motion, along with the factors that affect mechanical stability.

Many athletic skills require mechanical stability. © Susan Hall.

### EQUILIBRIUM

#### Torque

As discussed in Chapter 3, the rotary effect created by an applied force is known as torque, or moment of force. Torque, which may be thought of as rotary force, is the angular equivalent of linear force. Algebraically, torque is the product of force and the force's moment arm, or the perpendicular distance from the force's line of action to the axis of rotation:

T = Fd

torque

the rotary effect of a force about an axis of rotation, measured as the product of the force and the perpendicular distance between the force's line of action and the axis

moment arm

shortest (perpendicular) distance between a force's line of action and an axis of rotation

Thus, both the magnitude of a force and the length of its moment arm equally affect the amount of torque generated (Figure 13-1). Moment arm is also sometimes referred to as force arm or lever arm.

###### FIGURE 13-1

Which position of force application is best for opening the swinging door? Experience should verify that position C is best.

As may be observed in Figure 13-2, the moment arm is the shortest distance between the force's line of action and the axis of rotation. A force directed through an axis of rotation produces no torque, because the force's moment arm is zero.

###### FIGURE 13-2

The moment arm of a force is the perpendicular distance from the force's line of action to the axis of rotation (the door hinge).

Within the ...

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