Sorry to scare you but as we've just taken a look at inertia I thought I'd do this little snippet on 'moment of inertia' its important and useful in biomechanics, why? Well I'll tell you:
As you'll remember, inertia is a body's resistance to change in velocity and inertial force is the ficticious force that manifests in the presence of acceleration, proportional to the acceleration ( times the mass) but in the opposite direction.
Considering the inertia in this 1st case it is often quite convenient to just ignore inertial force. So say you want to push something in a straight line, like a sledge across the ice with your fat mate sitting on it. The sledge and your mate weigh 200kg and you apply a force of 500N to the centre of mass then the acceleration will be what?
Get out the handy equation f=ma - rearrange to find the acceleration a=f/m plug in the numbers we know 500/200 and viola a=2.5m/s/s. After a couple of seconds you stop pushing and he's going at 5m/s (that's his velocity) or 18kph. His momentum (mass x velocity) carries him along quite merrily, and lets say the ice/sledge interface has no friction, well then, after an hour he's hit a snow drift and has a long walk back. Very interesting, we knew a lot about his change in motion, the direction and displacement and didn't need to consider inertial forces at all.
But!
If we look at a podiatry related example and consider the leg:
Then the inertia is very important, why? Because how does a leg move? In an arc or rather an angular displacement.
The shape of the leg (without the foot) is rather like a baseball bat, fat at the hip end and getting thinner toward the ankle.
That means the CoM (what is the centre of mass? Bear with me) will be near the top of the leg and you'll remember that if we accelerate the mass, or centre of mass, then we have an inertial force in the opposite direction.
Centre of mass is, simply put, where everything balances with no net rotation. So if you have a see saw beam with equally spread out mass (or weight) then the balance point or fulcrum would be in the middle of the beam. But if the mass is mainly distributed about one end, like a leg, then the balance point will be near to the fat end and that's where the CoM is found.
So the CoM of the leg is in the proximal femur, let's say its 20cm from the hip joint. The flexor group of muscles flex the hip and the leg CoM experiences an angular acceleration and the inertial force produces a turning moment about the hip joint. In other words, as the inertia of the CoM resists the acceleration it produces a force that has a lever of 20cm to the hip joint and so this is equivalemt (equal and opposite) to the force that the muscles must apply to rotate the leg.
Are you keeping up? I'll do some diagrams tomorrow
Now, force x lever (or moment arm) = moment (or torque) - So, the torque produced by the inertial force on the lever arm of the femur to the hip joint is the inertial moment and this is equal and opposite to the torque applied by the muscles to rotate the leg about the hip.
All well and good, you can perhaps see the importance of considering the inertia in that example.
But wait!
What if the leg was fat at the tibial shank, like when we observe lymphoedema for instance?
Well where would the leg balance now? Perhaps the CoM of the leg would be nearer the knee, say 40cm from the hip joint. How does that effect the price of fish?
Well, if we accelerate the CoM at the same angular acceleration, lets just say acceleration for convenience now, then it will experience the same inertial force in the opposite direction. However, the moment arm is twice a long as in the former example and so the inertial moment will be twice a large. Therefore, the torque required to be applied by the muscles rotating the leg will also need to be twice as large.
No wonder those ladies, with stage 3 lympoedema, waddle and huff and puff and they walk along, imagine the extra energy required to produce twice the effort for the same amount of work. Oh blimey, energy and work, that's a topic on it own, but anyway, I hope you get the gist - 😂 Moment of inertia, a very important consideration when your looking at rotating levers.
Perhaps you might like to consider (in principle) the effect of the weight of a shoe on the performace of a runner - something to think about for the weekend 😎
Cheers
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