Impulsemomentum Relationship

Human movement occurs over time, so many biomechanical analyses are based on movement-relevant time intervals. For example, walking has a standardized gait cycle (Whittle, 2001), and many sport movements are broken up into phases (usually, preparatory, action, and follow-through). The mechanical variables that are often used in these kinds of analyses are impulse (J) and momentum (p). These two variables are related to each other in the original language of Newton's second law: the change in momentum of an object is equal to the impulse of the resultant force in that direction. The impulse-momentum relationship is Newton's Second law written over a time interval, rather than the instantaneous (F = ma) version.

Impulse is the effect of force acting over time. Impulse (J) is calculated as the product of force and time (J = F • t), so the typical units are Ns and lb-s. Impulse can be visualized as the area under a force-time graph. The vertical ground reaction force during a foot strike in running can be measured using a force platform, and the area under the graph (integral with respect to time) represents the vertical impulse (Figure 6.13). A person can increase the motion of an object by applying a greater im-

Figure 6.13. The vertical impulse (JV) of the vertical ground reaction force for a footstrike in running is the area under the force-time graph.

pulse, and both the size of the force and duration of force application are equally important. Impulse is the mechanical variable discussed in the following section on the "Force-Time Principle." In movement, the momentum a person can generate, or dissipate in another object, is dependent on how much force can be applied and the amount of time the force is applied.

Newton realized that the mass of an object affects its response to changes in motion. Momentum is the vector quantity that Newton said describes the quantity of motion of an object. Momentum (p) is calculated as the product of mass and velocity (p = m • v). The SI unit for momentum is kg-m/s. Who would you rather accidentally run into in a soccer game at a 5-m/s closing velocity: a 70- or 90-kg opponent? We will return to this question and mathematically apply the impulse-momentum relationship later on in this chapter once we learn about a similar kinetic variable called kinetic energy.

The association between impulse (force exerted over time) and change in momentum (quantity of motion) is quite useful in gaining a deeper understanding of many sports. For example, many impacts create very large forces because the time interval of many elastic collisions is so short. For a golf ball to change from zero momentum to a very considerable momentum over the 0.0005 seconds of impact with the club requires a peak force on the golf ball of about 10,000 N, or greater than 2200 pounds (Daish, 1972). In a high-speed soccer kick, the ball is actually on the foot for about 0.016 seconds, so that peak forces on the foot are above 230 pounds (Tol, Slim, van Soest, & van Dijk, 2002; Tsaousidis & Zatsiorsky, 1996). Fortunately, for many catching activities in sport an athlete can spread out the force applied to the ball over longer periods of time. The Impulse-Momentum Relationship is the mechanical law that underlies the Force-Time Principle introduced earlier in chapters 2 and 4. Let's revisit the application of the Force-Time Principle with our better understanding of linear kinetics.

Interdisciplinary Issue:Acute and Overuse Injuries

A very important area of research by many kinesiology and sports medicine scholars is related to musculoskeletal injuries. Injuries can be subclassified into acute injuries or overuse injuries.Acute injuries are single traumatic events, like a sprained ankle or breaking a bone in a fall from a horse. In an acute injury the forces create tissue loads that exceed the ultimate strength of the biological tissues and cause severe physical disruption. Overuse injuries develop over time (thus, chronic) from a repetitive motion, loading, inadequate rest, or a combination of the three. Injuries from repetitive vocational movements or work-related musculoskeletal disorders (WMSDs) are examples of chronic injuries (Barr & Barbe, 2002). Stress fractures and anterior tibial stress syndrome (shin splits) are classic examples of overuse injuries associated with running. Runners who overtrain, run on very hard surfaces, and are susceptible can gradually develop these conditions. If overuse injuries are untreated, they can develop into more serious disorders and injuries. For example, muscle overuse can sometimes cause inflammation of tendons (tendinitis), but if the condition is left untreated degenerative changes begin to occur in the tissue that are called tendinoses (Khan, Cook, Taunton, & Bonar, 2000). Severe overuse of the wrist extensors during one-handed backhands irritates the common extensor tendon attaching at the lateral epicondyle, often resulting in "tennis elbow."

The etiology (origin) of overuse injuries is a complex phenomenon that requires interdisciplinary research.The peak force or acceleration (shock) of movements is often studied in activities at risk of acute injury. It is less clear if peak forces or total impulse are more related to the development of overuse injuries. Figure 6.14 illustrates the typical vertical ground reaction forces measured with a force platform in running, step aerobics, and walking. Note that the vertical forces are normalized to units of bodyweight. Notice that step aerobics has peak forces near 1.8 BW because of the longer time of force application and the lower intensity of movement.Typical vertical ground reaction forces in step aerobics look very much like the forces in walking (peak forces of 1.2 BW and lower in double support) but tend to be a bit larger because of the greater vertical motion. The peak forces in running typically are about 3 BW because of the short amount of time the foot is on the ground. Do you think the vertical impulses of running and step aerobics are similar? Landing from large heights and the speed involved in gymnastics are very close to injury-producing loads. Note the high peak force and rate of force development (slope of the F-t curve) in the running ground reaction force. Gymnastic coaches should limit the number of landings during practice and utilize thick mats or landing pits filled with foam rubber to reduce the risk of injury in training because the rate of loading and peak forces are much higher (8 BW) than running.

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