Rotational Speed around a fixed point.

[Leader Bee]

Greetings SFN users.

 

New to the forums so a big hello, hopefully my first question will be a productive one.

 

I was sitting at work recently watching the clock tick by when it occurred to me...

 

The point of the hands closer to the centre must be moving slower than the extremeties of the hands?

 

What brought me to this conclusion is that the circumfrance of a circle closer to the centre has a shorter distance than a circumfrance of a circle further out from the centrepoint.

 

Consider if I was to walk around the same running track, once on the inside circumferance and the second time around the outside circumferance. The second time would take me longer (considering I walked at a constant speed on both laps ) so to compensate on the second lap I would run instead of walk to complete my lap in the same time I would have completed the first.

 

My questions are therefore:

 

1) what processes are in effect so that the tip of the minutehand stays in alignment with the centre.

 

2) if one part is moving at a quicker rate than the part closer the centre shouldn't there be a noticable drag or trailing tip, what is preventing this bending or lag time?

 

3) how can the speeds of the tip and the centrepoint be variable if they are running from the same and sole (non variable) powersource? I.e: the clock motor.

 

I imagine this same question could be applied to planetary bodies also but differeng compositions of internal structures would alter the answer ( solid core, liquid or gas, etc.)

 

Regards

[Sisyphus]

The hand is a solid, fairly rigid object. It's molecules are bonded together (the nature of the bond depends on the material). Move one, it exerts a force on every one touching it, which itself moves, and so on. Exert a torque ("spinning force") on one, the one next to it is carried along on a longer path, and the next, and so on.

 

There is indeed a very slight lag, because there is no such thing as a perfectly rigid object. It takes time for the motion to be successively transferred from the inside outwards. The maximum speed at which this motion can ever be transferred is the speed of light, but any material you're likely to see will be much, much slower than that (but still fast enough that it effectively seems perfectly rigid).

 

For your third question, I'd just ask why you think it shouldn't?

[Leader Bee]

3) how can the tip and centrepoint have a variable speed if they are powered by the same energy source?

 

The energy source isn't putting out 2 varying amounts of energy.

 

The only reason I could think that that there may be a difference in speed at each point is due to energy loss.

Edited July 2, 2009 by Leader Bee
Contradicts original post

[swansont]

3) how can the tip and centrepoint have a variable speed if they are powered by the same energy source?

 

The energy source isn't putting out 2 varying amounts of energy.

 

The only reason I could think that that there may be a difference in speed at each point is due to energy loss as it makes it's way towards the tip but taking into consideration that the part closer to the motor is moving slower this doesnt make sense to me. Surely the closer to the energy source the faster it should move due to less energy being lost at that point?

 

The answer is subtle but there's a clue in what Sisyphus explained.

 

There is no perfectly rigid object, so there is a slight bend as you move outward. That means there is both a force toward the center (centripetal force), required for circular motion, but also a tangential force, required to speed the arm up. This tangential force does work, and because the path is longer as the radius increases, it does more work as r increases, and being a maximum at the tip. Proximity to the energy source does not mandate that the energy transferred be a maximum there. Energy is transmitted through forces (i.e. doing work) and at the center the force is entirely centripetal. And centripetal forces do no work.

[J.C.MacSwell]

The answer is subtle but there's a clue in what Sisyphus explained.

 

There is no perfectly rigid object, so there is a slight bend as you move outward. That means there is both a force toward the center (centripetal force), required for circular motion, but also a tangential force, required to speed the arm up. This tangential force does work, and because the path is longer as the radius increases, it does more work as r increases, and being a maximum at the tip. Proximity to the energy source does not mandate that the energy transferred be a maximum there. Energy is transmitted through forces (i.e. doing work) and at the center the force is entirely centripetal. And centripetal forces do no work.

 

There should be a torque and an additional non centripetal reaction force at the center as well if the clock motor is accelerating the arm or compensating for drag.