Torque without pivot (Torque with only one force)

[cheahchungyin]

Imagine, I drop a stick with uniform mass horizontally towards the ground. There is only one force acting on it, which is the weight.

By common sense, I would know that the stick will not turn. However, mathematically there is a net torque if I set the pivot point on either side of the stick.

So what's the problem here?

 

[Doc Al]

Imagine, I drop a stick with uniform mass horizontally towards the ground. There is only one force acting on it, which is the weight.

By common sense, I would know that the stick will not turn. However, mathematically there is a net torque if I set the pivot point on either side of the stick.

So what's the problem here?

The problem is that you are using an accelerating point as your pivot. About such a point, the rate of change of angular momentum is not simply given by the net torque. There are other terms. (Which end up canceling that torque term, so you are left with no rotation. So your common sense was correct.)

 

[0xDEADBEEF]

The problem is, that angular momentum is a different concept than most people realize. If we talk about the conservation of angular momentum we mean the angular momentum off all moving mass around an arbitrary point in space. A point mass (which cannot rotate for more or less obvious reasons) flying past the origin at some distance has an angular momentum. A force acting on this mass will produce a torque changing the angular momentum. If you consider a stick centred at the origin that is hit by this mass it can start spinning an thus gain angular momentum from the point mass which loses it. The reason why we often only speak of torque and angular momentum around the centre of mass of objects is Steiner's theorem (aka. parallel axis theorem) which states that angular movements can be split into the rotation around an origin of an object's centre of mass plus the objects rotation around it own centre of mass.