1. 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)

2. 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

3. 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

4. Mechanical Advantage
MA = mechanical advantage

5. Levers

6. 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

7. First-Class Lever

8. Second-Class Lever

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

10. Third-Class Lever

11. Torques

12. Segment Torques

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

14. Static Analysis (cont.)

15. Static Analysis (cont.)

16. 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

17. Positive and Negative Work of Muscles

18. 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

19. Positive and Negative Muscle Power