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Rotational Overload – Rotational Inertia

November 10, 2021
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So how can light loads of 200-400 gm (7 to 14 oz) be called resistance strength training? How can the RPE be 25-30% (previous post) harder when sprinting with such loads as compared to an unloaded sprint? A lot of the explanation comes down to a concept called rotational inertia. So if you want to learn how rotational inertia contributes to rotational overload buckle up, the wheels are about to spin.


Inertia is the resistance of a body to change in motion and is a function of mass. For example, if you place 400 grams on your thigh as in Figure 1A, then your thigh is 400 gm heavier and therefore requires more muscular effort to accelerate and decelerate. Have a look at Figure 1B, where there is 400 grams placed on the thigh once more. So it weighs the same as Figure 1A. However, do you think it is requires more, less or the same muscular effort to get it going compared to A? It requires more as that loading has greater rotational inertia. Let me explain.

Rotational Inertia

So instead of inertia, rotational inertia is what we are really interested in when talking rotational overload with limb loaded wearable resistance (WR), and it is important to understand, if you are to overload with WR safely and effectively, so tune into his next paragraph. The formula for rotational inertia is I = mr2  where I = rotational inertia; m = mass; and, r = distance from axis of rotation. So let’s take the thigh as an example, we know the thigh has mass and therefore requires rotational force (torque) to move it. The larger the thigh mass the more muscular effort (torque) is required by the hip flexors and extensors. So by simply adding more WR to the thigh we increase the rotational inertia of the thigh, which means more muscular effort or turning forces/torques are required at the hip joint. But let's not forget the second part of the rotational inertia formula (r2), which translates to where we put the mass is really important. In fact this has more of an influence on rotational inertia (muscular effort) as any distance change is squared.

Figure 1: A 400 gm/14 oz load attached mid thigh (A) and distal thigh (B)

Let’s have a look at an example, what happens when we add 400 gm/14 oz to the thigh mid femur as shown in Figure 1A? I have modelled the rotational inertia associated with the thigh of a 86 kg/190 lB athlete. In Table 1 you can see the rotational inertia associated with a variety of loads when the loads are positioned mid-thigh (Figure 1A) and distal thigh (Figure 1B). So for a 400 gm/14 oz load, by shifting the same load 20 cm down the leg (Figure 1A to 1B), we have increased the rotational inertia of the limb from 4.7% to 12.1% because the load is further away from the axis of rotation (hip joint). We call this distal loading and load placement is one of the most important loading parameters to understand with WR, because for every cm/inch you move from the axis of rotation the distance is squared and hence this has a substantial effect on rotational inertia and therefore muscular work at the hip, in this example.

Figure 2: Effects of mid and distal thigh loading on rotational inertia

Take Home Messages

In summary, human motion is typically the product of rotation at the joints. To optimise strength gains and transference to the activities of interest, overloading these rotational movements makes a lot of sense. When limb loading, very light weights can provide substantial rotational overload to the musculature due to the concept of rotational inertia. By slipping a weight more distal to the rotating joint you can systematically and progressively overload the involved musculature without additional load. Such loading has many applications for injury resistance, return to play and sporting performance.