Spot my mistake

[Borodog]

So I made a rather embarrassing mistake in lecture yesterday (and believe it or not repeated it today, before finally spotting what was wrong after class).

The problem:

I specified a hexagonal nut being turned by a wrench, with a force of 10 N being applied perpendicular to the lever arm of 0.1 m, yielding a torque of 1 Nm. I further specified that the nut had a mass of 10g, and a radius of 1 cm, hence its moment of inertia would be something of order 10^-6 kg m^2. When you plug this into torque = I x alpha and solve for the angular acceleration, you get a ridiculous number, alpha = 10^6 rad/s^2. This is totally "unphysical" as we physicists say.

So where did I go wrong?

[m_the0ry]

Its not really a mistake, but the major counteracting force here is not the inertia of the nut but the friction force.

[Borodog]

[ QUOTE ]
Its not really a mistake, but the major counteracting force here is not the inertia of the nut but the friction force.

[/ QUOTE ]

Assume the nut is lubricated with rackenpinion molecules and rotates without friction. 10^6 rad/s^2 is still a totally ridiculous angular acceleration.

Keep looking.

[Borodog]

I really want to know if Sklansky can spot this. It doesn't really take any knowledge of physics beyond what is described in the OP.

[bluesbassman]

Are you assuming the wrench has no mass?

[Borodog]

[ QUOTE ]
Are you assuming the wrench has no mass?

[/ QUOTE ]

Bingo. The problem is not really about turning the nut at all; it's about rotating the wrench. The moment of inertia of the wrench about it's end is of order a million times greater than that of the nut. Hence your hand doesn't get chopped off by the wrench in a blinding blur when you try to turn the nut.

[btmagnetw]

i don't know what i just read, but it was awesome.

[Nielsio]

[ QUOTE ]
i don't know what i just read, but it was awesome.

[/ QUOTE ]

[SamIAm]

[ QUOTE ]
Hence your hand doesn't get chopped off by the wrench in a blinding blur when you try to turn the nut.

[/ QUOTE ]
I dunno. You've never seen me work around the house...

Good thread, borodog. That's an interesting brain-teaser.

[bluesbassman]

[ QUOTE ]
[ QUOTE ]
Are you assuming the wrench has no mass?

[/ QUOTE ]

Bingo. The problem is not really about turning the nut at all; it's about rotating the wrench. The moment of inertia of the wrench about it's end is of order a million times greater than that of the nut. Hence your hand doesn't get chopped off by the wrench in a blinding blur when you try to turn the nut.

[/ QUOTE ]

It would have been embarrassing not to spot that right away given my profession. /images/graemlins/grin.gif

I asked the question only because I thought you possibly considered the calculated angular acceleration too high even given a massless wrench, due to some additional, more subtle assumption.