Components of Torque (Moment of Force) r is the perpendicular distance from the line of action of a force to the pivot point The units of torque are newton-meters (Nm)

Rotational Analog of Newton’s Third Law For every torque applied by one body on a second, there is an equal and opposite torque exerted by the latter body on the former

Center of Mass The center of mass is the point about which the mass is evenly distributed It is the point about which the sum of torques is equal to zero

Mechanical Advantage MA = mechanical advantage

Levers

Classes of Levers First class: MA varies Second class: Favors the effort force MA > 1 (i.e., a smaller effort force can balance a larger resistive force) Third class: Favors range and speed of (MA < 1) movement

First-Class Lever

Second-Class Lever

Third-Class Levers The majority of musculoskeletal systems are in third- class levers These levers favor speed and range of movement

Third-Class Lever

Torques

Segment Torques

Static Analysis If angular acceleration is zero, the sum of moments (M) must equal zero This is known as static equilibrium

Static Analysis (cont.)

Static Analysis (cont.)

Effects of a Torque Applied over an Angular Displacement T = the applied torque   = the angular displacement over which the torque is applied The units of angular work, like the work due to linear forces, are joules (J) Work is a scalar quantity

Positive and Negative Work of Muscles

Angular Power We saw in Chapter 10 that power is the rate of change of work Angular power is the rate of change in angular work Units of power are watts (J/s) Power is a scalar quantity 17

Positive and Negative Muscle Power