Confusion on the concept of point of rotation

[Gourab_chill]

Homework Statement

I had a bit of confusion on the point of rotation of rolling bodies. When a body rolls, we apply the formula τ = Iα. But in order to compute the moment of inertia we need to know the point of rotation of the object. If the object rolls about it's bottom most point then we need to add a extra {MR}^{2} for most rolling bodies. So please explain how to determine the point of rotation for rolling bodies.

Relevant Equations

τ = Iα

--no explanation as conceptual error--

 

[jedishrfu]

While you're waiting for an answer, perhaps this will help:

http://hyperphysics.phy-astr.gsu.edu/hbase/rotwe.html

and this concerning the moment of inertia and center of mass:

http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html#pax

 

[Gourab_chill]

While you're waiting for an answer, perhaps this will help:

http://hyperphysics.phy-astr.gsu.edu/hbase/rotwe.html

and this concerning the moment of inertia and center of mass:

http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html#pax

I know the fundamental concepts but I'm confused only on the particular concept I've stated above.

 

[Cutter Ketch]

$\Gamma = I \alpha$ will hold true for any axis of rotation you choose, even one that isn’t inside the rotating body. The inertia I can be constructed for whichever axis you choose. In fact, you can calculate I for the center of the cylinder and then use that to find I about some other axis by the parallel axis theorem.

So the question is which axis should you choose for evaluating the motion? For a rolling object there is a force of constraint. The rolling friction will be whatever magnitude force is required to prevent slipping. Since you don’t know how big the force of friction might be, putting the axis of rotation at the point of contact with the road will get that unknown out of your torque calculations.