- #36
Urmi Roy
- 753
- 1
BobbyBear said:I'm thinking of the case of the wheel as a limiting case of the block of n sides (regular polygon) as the No. of sides goes to infinity.
Well,this aspect never struck my mind,so I never really thought in this direction--it opens a new route for thought.
BobbyBear said:So okay, let me accept that for the case of the wheel the friction force is not equal to (in magnitude) ...and then impose the no-slipping condition through which I can relate the angular acceleration of the wheel to the linear acceleration of the centre of mass (as I did previously except that I had assumed f to be known), and from there solve for f. I think this would be the procedure you're indicating?
I agree this is the best way to deal with it mathematically,but again, we are assuming that there is no slipping and then proceeding on these lines--I would rather like to refer to this in a less mathematical way,and instead,try to find out what is actually going on with all our forces,and their individual effects.
In our book, we find an entire section, called the "Paradox of the rotating wheel" in which the big question is, why does the wheel not accelerate inspite of the static frictional force providing the requisite torque. Here, the author brings in rolling friction,which according to him provides an opposing torque and hence the wheel does not accelerate, but as stated earlier, since we are considering rigid bodies, we ideally should not be bringing in rolling friction,and as clarified by BobbyBear, rolling friction is not an independant force.Further, in all other sources,they don't state anything about rolling friction.
Now, Doc Al said that the wheel on the ramp does indeed accelerate--perhaps so,but a similar situation arises in case of a wheel on level ground,where the force provoking the rolling of the wheel and the frictional forces both provide accelerating torque--but still the wheel does not accelerate.
This was actually the issue addressed in my book,that I referred to earlier.
Again I admit that frictional forces doing work sounds pretty bizarre,and as Doc Al clarifed,it doesn't actually do any work,however I fail to understand how this is so,since the friction does try to provide the wheel angular acceleration,even in the case of a wheel on level ground.According to Newton's second law applied to rotational mechanics,the friction should be doing work in this case.