Key words: Impulse, momentum, purposefully slow, time-under-tension.

Performing exercise under any type of resistance is broadly defined as resistance training (Newton, 1999). Because the effect of the earth's gravity is universally present on earth, the physics of resistance training with a constant load (isoinertial) are relatively simple. What are not simple, however, are the ultimate physiological and morphological effects of resistance training. Several variables can be manipulated in resistance training programs to bring about a specific desired result (Wernbom et al., 2007). Load, number of sets, number of repetitions per set, number of exercises, mode (machine or free weight), repetition speed, rest period length, exercise order, training frequency, and the specific exercises selected can all be manipulated to promote a precise desired outcome. Such outcomes include increased muscular endurance, muscle size, increased muscle strength, increased muscle power, and decreased relative body fat. It is unlikely that a single program or method will be effective in realizing all of the possible benefits of resistance training equally.

Training programs have been developed that aim to regulate repetition speed, specifically recommending purposefully slow actions (~10s for the concentric and ~4-10s for eccentric portions). Much of the support for such programs exists only in lay media (Brzycki, 1995; Hutchins, 2001; Wescott, 1999), with little empirical evidence (Greer, 2005). The arguments for prescribing such training programs often use terminology that is not soundly based in classical physics, or is derived from other resistance training/testing modalities uncommon to that of question (i.e. isokinetic, in vitro or in situ studies). For instance, protocols such as this have been confusingly called "low force" (Hutchins, 2001) while at the same time touted as having "more muscle tension" (Wescott et al., 2001), "more muscle force" and "less momentum" (Wescott, 1999). It is the purpose of this paper to correctly describe the mechanical aspects of such training, as these programs have been used in several empirical studies (Greer, 2005). We will also provide a case example where the mechanical properties of a common resistance training exercise will be shown. Specific training studies will not be reviewed in detail as they are primarily interested in physiological effects (for such a review see Greer, 2005), but we hope that this mechanical review will lay the groundwork for productive evaluation of resistance training over the load and velocity spectrum.

Force-velocity relationship
The force-generating capability of the neuromuscular system under maximal voluntary or involuntary activation is dependent on movement velocity, as illustrated through the force-velocity (F-V) relationship (Fitts and Widrick, 1996; Gülch, 1994). Essentially, the F-V relationship is a hyperbolic curve constructed from the results of numerous experiments describing the dependence of force on the velocity of movement (Hill, 1953). This relationship has been examined in vitro, in situ, and in vivo. The force that the muscles can produce decreases at a given pre-determined velocity (computer-controlled in vivo isokinetic/isovelocity modalities) as that velocity increases. The F-V relationship assumes that at a given velocity, the muscles are generating the maximum force possible. A similar load-velocity relationship is also demonstrated in isoinertial, in vivo exercise with maximal voluntary acceleration (Cronin et al., 2003). In this case, as the external load (i.e. mass) increases, the maximal velocity that such load achieves decreases. The load-velocity relationship assumes that the movement velocity is the maximum possible for the given load. The likely source of the F-V relationship is the fact that when the cross-bridge cycling speed increases, there are fewer cross-bridges formed to develop force (Gülch, 1994). This relationship between force and velocity is what may have prompted some to suggest that the voluntary muscle action should be carried out over a 10-s period so that the velocity is low, thereby increasing force (Wescott, 1999).

Impulse and momentum
The relationship between force and velocity for a constant mass (such as is encountered in free-weight training) is given in the relationship between impulse and momentum. A constant mass under the influence of a force can be expressed with Newton's second law represented by equation 1.

When a force acts upon the object from a time period from t₁ to t₂, equation 1 can be integrated in time to obtain equation 3.

Equation 3 defines linear impulse (I), and is equal to the change in linear momentum, as shown in equation 4.

As mass is constant during free-weight resistance training, a greater impulse will result in a greater velocity.

In human movement, force is required first to maintain static equilibrium and second to generate acceleration. The force required to maintain static equilibrium is equal to an object's mass multiplied by gravitational acceleration. Additional force results in acceleration of a mass or a change in momentum. These components of acceleration are described in equation 5:

Arguments for purposefully slow (PS) training
Muscle force: While PS proponents vary in their reasoning for suggesting this method, the basic premise is that when the weight is moving quickly, the muscles will not be able to exert as much force and thus the training effect will be diminished (Brzycki, 1995; Wescott, 1999). While true that the muscles will not produce as much force at the higher velocities during maximum effort velocity-controlled actions, the previous statement ignores the requisite force to initiate high velocity movements for a given load in an isoinertial condition. In addition, the aforementioned F-V relationship was derived under conditions of maximal acceleration (maximal voluntary muscle activation), and thus differs from intentionally slow movements. An attempt to reduce the speed of motion subsequently reduces the force expressed (Keogh et al., 1999).

Metabolic stimulus: Metabolic factors influenced by muscle contraction include H+ production, sarcoplasmic calcium concentration, intramuscular oxygen concentration, growth factors, cytokines, and availability of hormones and receptors (Crewther, Cronin, and Keogh 2006; Rennie et al., 2004). Modifications to any one of these metabolic factors during exercise may alter signal transduction pathways and hence modify gene transcription for muscle growth (Rennie et al., 2004). Potential strength adaptations due to acute metabolic stimuli have recently been reviewed elsewhere (Crewther et al., 2006) and arguments for the importance of metabolic factors in resistance training adaptation have been made (Kawada and Naokata, 2005; Kanehisa et al., 2002; Schott et al., 1995; Smith and Rutherford, 1995). The metabolic hypothesis has not yet been examined in conjunction with PS training studies; therefore these ideas are currently speculative for this type of training.

Time-under-tension: Movements performed at low velocities prolong the time of contraction in each repetition for a given range of motion (time-under-tension; TUT). Proponents of PS training regard this increased time as a positive characteristic to stimulate training adaptation (Wescott et al., 2001). TUT can be considered a manner by which to prescribe a dose of resistance exercise (Tran and Docherty, 2006), which is crucial as the optimal dose for weight training is subject to tremendous debate (Carpinelli and Otto, 1998; Stone et al., 1998). PS advocates suggest that this time dose or TUT is of greater importance than the actual load lifted, which could be related to the fact that perceived effort in PS and normal training session have been shown to be similar (Egan et al., 2006). This rationale originates from the hypothesis of a direct relationship between the duration of contraction and metabolic stimulus, but this hypothesis has not been supported in studies examining PS exercise (Gentil et al., 2006; Hunter et al., 2003; Keogh et al., 1999).

A potential caveat of increased TUT is that the load must be decreased to perform a successful 10-s concentric contraction as compared to a maximal acceleration repetition (i.e. decreased TUT). This is concerning as the load, or mechanical stimuli, has been suggested to be of critical importance for inducing adaptation (Dudley et al., 1991; Hortobagyi et al., 1996; McDonagh and Davies, 1984). Evidence for the load used in resistance exercise emphasizing hypertrophy indicates a possible optimal threshold of 85% 1RM (Fry, 2004), but the multitude of acute training variables that may be altered in addition to load make a precise recommendation difficult. However, the reduced load advocated by PS might be less effective for hypertrophy due to the load constraints. This reduction in load is seen by PS advocates as inconsequential to the ultimate physiological effects. However, a basic premise of tissue adaptation (i.e. Wolff's and Davis' Laws (Biewener and Bertram, 1994) is that a minimum threshold of force is required to elicit adaptation. The notion that load is peripheral in its importance is in direct opposition to other authors' demonstrating the magnitude of mechanical stress (i.e. load) is most responsible, in the context of exercise volume, for strength gains and muscle hypertrophy (Dudley et al., 1991; Hortobagyi et al., 1996). Please note that although related, load and muscle force are not equal, as propulsive forces can differ.

Increasing TUT for an exercise session can be accomplished by simply increasing the number of total repetitions of maximal-acceleration exercises (increased volume-load; Tran and Docherty, 2006). This would ultimately increase the time that the muscle has been under tension for that session, but the force output of the muscle will have been greater due to the relatively larger loads. The complex relationship between load and TUT requires further investigation.

Resistance training applications: Forms of resistance training fall within a continuum from slow to fast velocities. Resistance training such as powerlifting (relatively slow) and weightlifting (relatively fast) are quite far apart on this continuum. Weightlifting (WL) is the sport by which athletes attempt to lift maximal weight in the snatch and clean and jerk (Chiu and Schilling, 2005). WL is characterized by high accelerations and fast velocities due to the inherent nature of the sport by which a loaded barbell is moved from the ground at an initial velocity of '0' to an eventual overhead position. Successful performances of these lifts necessitate great velocities and thus great power (Garhammer, 1980; 1993). However, the relative loads (resistance) are not as great as seen in the sport of powerlifting (PL). PL is comprised of the bench press, squat, and deadlift exercises, and PL is performed at substantially lower velocities than WL. Elite PL records exceed 400kg in each of their respective lifts (Kraemer and Koziris, 1994). While these lifts begin with an explosive muscle contraction (high RFD), the overall velocity is slow due primarily to the high load (Brown and Abani, 1985; Garhammer and McLaughlin, 1980). Both PL and WL typically involve maximal acceleration, with the resultant velocity a function of the load lifted, and it has been suggested that it is the intent to maximally accelerate the load is common amongst PL and WL (Behm and Sale, 1993). In fact, PL and WL display similar levels of strength on some movements (McBride et al., 2002). Analogous to PL, PS training employs similar low velocities, but with substantially less resistance, as the velocity is deliberately slow (low acceleration). Considering these unique features, a simplistic case of the impulse-momentum relationship can be used to conceptually compare these forms of resistance training (Table 1). The relationships between force and various modes of resistance training identified in Table 1 exposes the potential for superior force production for WL and PL, but not with PS training. These conceptual relationships have been substantiated with lower eccentric and concentric forces seen in deliberately slow repetitions, as compared with those done with no restrictions on speed (Keogh et al., 1999).