After completing this chapter, you will be able to:

• Define torque, quantify resultanttorques, 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.

## 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: 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 human body, the moment arm for a muscle with respect to a joint center is the perpendicular distance between the muscle’s line of action and the joint center (Figure 13-3). As a joint moves through a range of motion, there are changes in the moment arms of the muscles crossing the joint. For any given muscle, the moment arm is largest when the angle of pull on the bone is closest to 90˚. ...

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