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Indeed, unbalanced throwing knives are used, but I have read that balanced throwing knives are easier to use, because due to their geometric center being the same as their center of mass. Why would this make them easier to use? Is there some issue of unequal wind resistance?

To clarify, I do want to the consider the case where the knife is thrown with the intent of spinning. Is it just the case that gravity will cause a torque that will mess up the flight pattern?

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    $\begingroup$ My guess is that a knife that isn't "balanced", when thrown, will tumble irregularly rather than cleanly spinning. This would depend on the complete shape of the knife, rather than the wind resistance. $\endgroup$ – Daniel Griscom Dec 7 '15 at 13:49
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    $\begingroup$ In general any rigid body will have three principle axes (a coordinate system along these directions will yield a diagonal moment of inertia tensor). The actual moments of inertia for the body spinning about each axis will differ. The rotations about the axes with the maximum and minimum moments of inertia are stable while rotation about the intermediate axis is unstable (prone to tumbling). The proof of this statement is frequently a homework assignment in advanced courses on classical mechanics. Most knife throwers choose the axis of maximum inertia for the axis of spin (no tumbling). $\endgroup$ – Lewis Miller Dec 7 '15 at 16:46
  • $\begingroup$ So is this, or is this not the reason? Does shifting the balance point really cause the desired axis to turn into an unstable axis? $\endgroup$ – Bob Dec 10 '15 at 9:41
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    $\begingroup$ I guess the point is that with a really unbalanced object it may be difficult to determine (by inspection) the principle axes. If a spin direction is chosen that includes a non-minimal component along the unstable (intermediate) axis then tumbling will occur. $\endgroup$ – Lewis Miller Dec 16 '15 at 21:36
  • $\begingroup$ In the case of a balanced knife isn't the axis of rotation not the minimum? I would expect that axis to be the longitudinal one. $\endgroup$ – Bob Dec 17 '15 at 18:36
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Consider the following diagram:

Unbalanced knife in flight.

The knife's centre of gravity (CoG, indicated as +) is towards the handle, so it's poorly balanced.

Now the thrower exerts a force $F$ in the direction of the target and this causes acceleration acc. Newton:

$$F=ma$$

After release the knife has a velocity vector $\vec{v}$ in the direction of the target and apart from gravity (and a small amount of air drag) no forces act on the knife.

Acc. Newton's Law the knife will now carry on on its trajectory, apart from starting to fall to the floor due to the weight ($mg$).

There's no reason to believe the knife will start tumbling, rotating, moving upwards or show any other unexpected behaviour, regardless of whether it is well balanced or not. That is what Newton's Law of motion tell us.

I believe (subjectively and based on my own experience) that balanced knives are easier to use as kitchen implements but that has nothing to do with in-flight properties.

Edit:

I'm sorry, I did mean that I wanted to consider the case where the knife is thrown to spin. I'll fix my question.

We can consider two different types of spin:

a) The knife rotates (spins) around its axis of flight:

This kind of spin is similar to spin imparted on bullets by means of barrel rifling. This imparts on the projectile extra kinetic energy (rotational energy in this case) and increases its resistance to side-wind. But unless significant force or torque acts on the projectile, Newton tell us that its state of motion (trajectory, speed and spin) will not change, balanced or not (bullets, e.g. aren't balanced).

b) The knife tumbles about an axis perpendicular to the flight path:

Think boomerang but without the specific shape and consequent effects of drag. Again, this state of rotation could only be disturbed by means of significant external forces or torques, as anyone who has ever thrown a stick for a dog will have experienced. Balance does not change this.

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  • $\begingroup$ I'm sorry, I did mean that I wanted to consider the case where the knife is thrown to spin. I'll fix my question. $\endgroup$ – Bob Dec 7 '15 at 4:02
  • $\begingroup$ @Bob: Hi Bob, I've edited my answer. $\endgroup$ – Gert Dec 7 '15 at 16:28

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