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Posted by: brer Aug 19 2005, 02:06 PM

So last night we were working on rotational motion and all i could think about was the crank in my motor and my car going around a corner..
anyone want to help explain this to me?


An object spinning at a constant speed has less acceleration at each consecutive point as you move further out from the center.
acceleration being related to the radius of the rotational orbit and the constant change in directional velocity.


Makes me car sick just thinking about it.

Posted by: qa1142 Aug 19 2005, 02:08 PM

Posted by: brer Aug 19 2005, 02:10 PM

i'm in way over my head.
see if i can swim to the surface.

Posted by: ArtechnikA Aug 19 2005, 02:36 PM

QUOTE (brer @ Aug 19 2005, 04:06 PM)

anyone want to help explain this to me? An object spinning at a constant speed has less acceleration at each consecutive point as you move further out from the center. acceleration being related to the radius of the rotational orbit and the constant change in directional velocity.

so what part of that is not clear to you? you explained it perfectly.

look at it this way:

picture a big turntable - like a record player (what are those?) or a playground carousel.

put an accelerometer 1' away from the center. it will show an acceleration vector toward the rotational center. because its angular velocity is large, it will show a large acceleration.

move the accelerometer out 30'. the acceleration vector still points in, but the angular change is smaller, and will show a smaller acceleration.

at infinity, the outer edge of the spinning disk is going in a straight line :-)

Posted by: lapuwali Aug 19 2005, 02:38 PM

Acceleration isn't just a change in speed, it's a change in VELOCITY, which is NOT the same thing. Velocity includes direction as well as speed. Any point on a spinning object is undergoing a constant change in velocity, as it's not going straight, but turning. The acceleration is along the radius of the turn. This is why you feel yourself getting pulled outwards when turning, and it is this force that the tires are resisting.

For a given speed, a larger radius of turning gives a lower change in velocity, and thus a lower acceleration. Going straight is the same as turning on an infinite radius, so zero change in velocity. Spinning an object faster is the same as increasing your speed around the same corner.

Posted by: brer Aug 19 2005, 03:05 PM

that was from my notes.

He's about 5 seconds away from erasing the board at any given moment.
Holds the eraser in one hand, the pen in the other.

Posted by: brer Aug 19 2005, 03:08 PM

which is why doing 60 through a 20mph turn is different than a 40mph turn. Tighter radius at the same speed.

See, i knew this was 914 related!

Posted by: Howard Aug 19 2005, 03:09 PM

QUOTE (brer @ Aug 19 2005, 01:06 PM)

So last night we were working on rotational motion

Are we talking about the same thing?

Posted by: Tom Perso Aug 19 2005, 03:13 PM

Sounds like someone is in a Dynamics class....

I forgot that as soon as I passed...

Tom

Posted by: bondo Aug 19 2005, 03:26 PM

Acceleration is a change in velocity, and velocity includes direction.. (think vectors here) so if you're going 60 mph north, and decide to turn right to be heading east while maintaining the same speed (speed is independent of direction), your northward velocity goes from 60 to zero, and your eastward velocity goes from zero to 60. The tighter the turn, the faster that change happens, and the greater the acceleration, as acceleration is change in velocity over time.

The "centrifugal" force you feel in a turn is a result of your body trying to continue in the same direction at the same speed, due to intertia.

Posted by: bondo Aug 19 2005, 03:37 PM

I'm confused by the spinning object situation...

If something is spinning at x RPM, every point on it is changing direction at the same rate. The points farther from the center are moving at a faster speed, but their direction is changing at the same rate as points close to the center. It seems to me that the outside points should have GREATER acceleration if you're looking at constant RPM.

This also makes sense in a real world sense as it's trickier to make large hign rpm rotational devices than small ones. Gyroscopes also put most of the mass on the outside. Hmm..

Posted by: phantom914 Aug 19 2005, 03:46 PM

QUOTE (bondo @ Aug 19 2005, 01:37 PM)

I'm confused by the spinning object situation... If something is spinning at x RPM, every point on it is changing direction at the same rate. The points farther from the center are moving at a faster speed, but their direction is changing at the same rate as points close to the center. It seems to me that the outside points should have GREATER acceleration if you're looking at constant RPM. This also makes sense in a real world sense as it's trickier to make large hign rpm rotational devices than small ones. Gyroscopes also put most of the mass on the outside. Hmm..

You are correct. Acceleration is (V^2)/r (sorry about the poor notation). V = velocity, r = radius. A point twice as far from the center as another point would have twice the velocity and twice the radius. So you would have twice the acceleration for the point further out in this example. A point three times further out would have three times the acceleration etc.....


Where did the :Nerd Alert: smilie go?

Andrew

Posted by: Sammy Aug 19 2005, 03:52 PM

as soon as i started reading the other replies it clicked what he was talking about so I deleted my post. Who knew that the stuff I tried so hard to forget 25 years ago would be 914 related?

Posted by: Dr. Roger Aug 19 2005, 03:54 PM

QUOTE (bondo @ Aug 19 2005, 01:37 PM)

I'm confused by the spinning object situation... If something is spinning at x RPM, every point on it is changing direction at the same rate. The points farther from the center are moving at a faster speed, but their direction is changing at the same rate as points close to the center. It seems to me that the outside points should have GREATER acceleration if you're looking at constant RPM. This also makes sense in a real world sense as it's trickier to make large hign rpm rotational devices than small ones. Gyroscopes also put most of the mass on the outside. Hmm..

The spinning object thing is a perfect analogy.

Your ice skating and initiate a spin, with your legs and arms swinging out as far as you can stretch. Rotating at 20 RPM.

Then take those "objects" (arms and legs) farthest from the center and bring them in closer to your axis.....

Huge acceleration. 60 RPM.

Why did it do that?

Posted by: bondo Aug 19 2005, 05:03 PM

QUOTE (rogergrubb @ Aug 19 2005, 02:54 PM)

QUOTE (bondo @ Aug 19 2005, 01:37 PM) I'm confused by the spinning object situation... If something is spinning at x RPM, every point on it is changing direction at the same rate. The points farther from the center are moving at a faster speed, but their direction is changing at the same rate as points close to the center. It seems to me that the outside points should have GREATER acceleration if you're looking at constant RPM. This also makes sense in a real world sense as it's trickier to make large hign rpm rotational devices than small ones. Gyroscopes also put most of the mass on the outside. Hmm.. The spinning object thing is a perfect analogy. Your ice skating and initiate a spin, with your legs and arms swinging out as far as you can stretch. Rotating at 20 RPM. Then take those "objects" (arms and legs) farthest from the center and bring them in closer to your axis..... Huge acceleration. 60 RPM. Why did it do that?

Exactly.. but that's the opposite of the original statement:

QUOTE

An object spinning at a constant speed has less acceleration at each consecutive point as you move further out from the center. acceleration being related to the radius of the rotational orbit and the constant change in directional velocity.

Posted by: SirAndy Aug 19 2005, 05:07 PM

QUOTE (brer @ Aug 19 2005, 01:06 PM)

Makes me car sick just thinking about it.

think about it this way:

the harder you think about it, the *closer* you get to the "center" of this problem, the more it makes your head spin ...

voila!
Andy

Posted by: brer Aug 19 2005, 05:11 PM

the outlying mass of arms and legs have greater velocity, covering more distance per revolution.
pulling them inward transfers the velocity of those objects to a smaller radius, decreasing the amount of time for one rotation........

in other words, keep your limbs inside the car and maybe i can corner faster.

Posted by: Rotary'14 Aug 19 2005, 05:13 PM

what if "D", "O", "G", spelled cat?

Whoa,, now that's some deep sh**!

Posted by: tdgray Aug 19 2005, 05:19 PM

OMG... Brain cramp... brain cramp

I cannot fathom your lofty ideas...I am but a mere accountant... with three degrees. WTF are you people talking about

Posted by: rhodyguy Aug 19 2005, 05:20 PM

those playground merry-go-rounds spin much too quickly if you sit in the center. if you go to the outer edge, the g-forces can kill you. you travel further, but slower, before you die.

k

Posted by: kwales Aug 19 2005, 08:30 PM

The correct answer is it all depends on your plane of reference.

Are you in the car or out of the car?

One is more difficult than the other.

Don't forget the earth spins too...

Better factor that in as well as galactic rotation and galactic drift....

Are you swimmy headed yet?

Ken

Posted by: brer Aug 20 2005, 10:01 PM

while studying today i found the math for it.
for those who are curious the formula is

Ar = (2Pi r)(2Pi r)/(T)(T)r

acceleration in rotation is equal to (2Pi times the Radius) squared over (Time for 1 rotation) squared times the Radius

which means,

at one revolution per second, and object rotating with a one meter radius has an acceleration of 39.5 m/sec(squared)

the same object rotating with a radius of 2 meters has an acceleration of 78.9 m/sec (squared) twice as much nearly!

there is a radius doubled, which lowers the Ar. But the speed of the object went from 6 m/sec up to 19 m/sec which raised the Ar.

that means the way i wrote it in the beginning was wrong.

guess i learned something.




so whats the difference between an engine with a long stroke vs. short stroke. The long stroke should have more acceleration going on, so does its lifespan reflect that? engine people know.

Posted by: SirAndy Aug 20 2005, 10:07 PM

QUOTE (brer @ Aug 20 2005, 09:01 PM)

so whats the difference between an engine with a long stroke vs. short stroke. The long stroke should have more acceleration going on, so does its lifespan reflect that? engine people know.

if i recall correct, the long stroke got more low end torque ...

Andy