Dumb wheel physics question

A friend was looking at the current thread about standing-start
downhill coasting tests.

He asked me whether the mass of the tires would make a difference.

I cleverly replied, "Huh?"

He expanded his question to something like this:

Given the same CRR and wind drag, will a wheel with more mass on its
rim (heavier tire) coast downhill from a standing start faster,
slower, or the same as the less massive wheel?

I cleverly replied, "Er . . ."

I'm hoping that RBT posters who like physics and equations involving
rotating masses will help me flesh out my answer.

Do the light and heavy tire behave the same way as a BB and a bowling
ball, which fall at the same speed in a vacuum?

Or do the miserable things accelerate differently because of the
rotation involved?

Cheers,

Carl Fogel

Some of the kinetic energy is in the spinning wheel, at the bottom
of the hill, so the bike itself has to be going forward slower by
that amount of energy. More mass in the rims, more energy in the
spinning wheel, and less in forward movement.
--
Ron Hardin
[email hidden]

On the internet, nobody knows you're a jerk.

http://www.todayinsci.com/

if one adds weight continuously to a wheel's rim, will the wheel spin
continuously?
or is that a different newton?

Quoted post said:

http://www.todayinsci.com/

if one adds weight continuously to a wheel's rim, will the wheel spin
continuously?
or is that a different newton?

CLICK "PERPETUAL MOTION" ON BOTTOM LEFT

On Thu, 29 Mar 2007 08:23:27 GMT, Ron Hardin <[email hidden]>

Quoted message said:

Some of the kinetic energy is in the spinning wheel, at the bottom
of the hill, so the bike itself has to be going forward slower by
that amount of energy. More mass in the rims, more energy in the
spinning wheel, and less in forward movement.

Dear Ron,

Another email from my friend just boiled the question down by
eliminating the bike and asking me to place my bet:

Two hoops of identical dimensions, one made of aluminum, the other of
steel, roll down an incline in a vacuum from a standing start.

If they were balls falling in a vacuum, it would be a tie because the
mass accelerates at the same rate, no matter how much there is of it.

Your explanation for the denser-heavier tire being slower sounds good
to me at first . . .

Until I wonder if the extra energy is supplied by the extra
gravitational pull on the extra mass, so it all cancels out, and hoops
of the same dimensions (and CRR) will accelerate uniformly down a
slope in a vacuum.

But Ron Ruff says (I think) that a heavier wheel is a little slower
down the slope in some model that he worked up, so that's two votes
from two Rons for heavier being slower down the slope.

So then I wonder if that means that a heavy enough wheel would refuse
to move at all down the slope, while a light enough wheel would reach
the speed of light. (I'm pretty sure that this logic must have a
gaping hole in it somewhere, but I'm floundering.)

I'm beginning to wonder if my friend has some famous damn experiment
up his sleeve. The only demonstration that I remember showed that
solid spheres roll faster down the same slope than solid disks, which
in turn roll faster than hoops--nothing about whether a denser hoop
rolls faster, slower, or the same speed down a hill as lighter hoop.

Cheers,

Carl Fogel

ANCHOVIES?

Quoted message said:

On Thu, 29 Mar 2007 08:23:27 GMT, Ron Hardin <[email hidden]>

Quoted message said:

Some of the kinetic energy is in the spinning wheel, at the bottom
of the hill, so the bike itself has to be going forward slower by
that amount of energy. More mass in the rims, more energy in the
spinning wheel, and less in forward movement.

Dear Ron,

Another email from my friend just boiled the question down by
eliminating the bike and asking me to place my bet:

Two hoops of identical dimensions, one made of aluminum, the other of
steel, roll down an incline in a vacuum from a standing start.

If they were balls falling in a vacuum, it would be a tie because the
mass accelerates at the same rate, no matter how much there is of it.

Your explanation for the denser-heavier tire being slower sounds good
to me at first . . .

Until I wonder if the extra energy is supplied by the extra
gravitational pull on the extra mass, so it all cancels out, and hoops
of the same dimensions (and CRR) will accelerate uniformly down a
slope in a vacuum.

But Ron Ruff says (I think) that a heavier wheel is a little slower
down the slope in some model that he worked up, so that's two votes
from two Rons for heavier being slower down the slope.

So then I wonder if that means that a heavy enough wheel would refuse
to move at all down the slope, while a light enough wheel would reach
the speed of light. (I'm pretty sure that this logic must have a
gaping hole in it somewhere, but I'm floundering.)

I'm beginning to wonder if my friend has some famous damn experiment
up his sleeve. The only demonstration that I remember showed that
solid spheres roll faster down the same slope than solid disks, which
in turn roll faster than hoops--nothing about whether a denser hoop
rolls faster, slower, or the same speed down a hill as lighter hoop.

Cheers,

Carl Fogel

Tonights homework: study chapter nine and work examples in section 9.3

http://www.lightandmatter.com/html_books/1np/ch09/ch09.html#Section9.3

http://wwwrses.anu.edu.au/~david/bikes/

If you don't understand the math, spend several years learning the
prerequisites.

If necessary, turn back the clocks and get a BS in physics next time
through life. Then restudy it all continuously throughout life, or
else it will all go away, as in my case. I recall the college
bookstore had some nifty books filled with these sorts of problems
that nutured my fascination in physics and led to that as my choice of
major. Unfortunately they're under copyright, and there doesn't
appear to be quality sources of elementary study of physics online.
Wikibooks textbooks appears pretty much filled with stubs waiting for
generous teachers to fill in the blank spaces. But it's comforting to
know the quality authors/teachers and publishers are able to assure
their long-term financial comfort by charging me dearly for their
material. Esp. the publishers and their current shareholders.

Bill Westphal

Quoted message said:

A friend was looking at the current thread about standing-start
downhill coasting tests.

He asked me whether the mass of the tires would make a difference.

I cleverly replied, "Huh?"

He expanded his question to something like this:

Given the same CRR and wind drag, will a wheel with more mass on its
rim (heavier tire) coast downhill from a standing start faster,
slower, or the same as the less massive wheel?

I cleverly replied, "Er . . ."

I'm hoping that RBT posters who like physics and equations involving
rotating masses will help me flesh out my answer.

Do the light and heavy tire behave the same way as a BB and a bowling
ball, which fall at the same speed in a vacuum?

Or do the miserable things accelerate differently because of the
rotation involved?

Heavier tire will be slower. The limiting cases are solid cylinder:
forward speed is 1.15*sqrt(g*h) and hollow cylinder: forward speed is
sqrt(g*h) where g is the acceleration due to gravity and h is the
height of the hill. The heavier the tire, the closer you are to the
hollow cylinder case and the lower the speed.

Formulae are straight from a physics text book.

Orin.

Quoted message said:

http://www.todayinsci.com/
if one adds weight continuously to a wheel's rim, will the wheel spin
continuously?
or is that a different newton?

Like a water driven mill?
--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

Quoted message said:

A friend was looking at the current thread about standing-start
downhill coasting tests.
He asked me whether the mass of the tires would make a difference.

."differently because of the

Quoted message said:

rotation involved?

For a given total mass the faster wheel will be the one with the least
moment of inertia. So, it will be the one with its mass located as
near as possible to its axis of rotation.

Sergio
Pisa
(the town of Galileo Galilei)

Quoted message said:

Until I wonder if the extra energy is supplied by the extra
gravitational pull on the extra mass, so it all cancels out, and hoops
of the same dimensions (and CRR) will accelerate uniformly down a
slope in a vacuum.

Yep. Things are a lot simpler in a vacuum. The equation I used for
calculating the transient motion for a cyclist is:

a=P/Mi/V- CdA*Da*V^2/2/Mi- g*G*M/Mi- g*Crr*M/Mi

In a vacuum, and no power input, the only terms left are:

a= -g*G*M/Mi- g*Crr*M/Mi where g is gravitational acceleration, G is
the grade, M is the static mass, and Mi the inertial mass. So the
acceleration will be the same if M/Mi is the same for both.

Quoted message said:

So then I wonder if that means that a heavy enough wheel would refuse
to move at all down the slope, while a light enough wheel would reach
the speed of light. (I'm pretty sure that this logic must have a
gaping hole in it somewhere, but I'm floundering.)

They will both reach the speed of light at infinity.

Quoted message said:

I'm beginning to wonder if my friend has some famous damn experiment
up his sleeve. The only demonstration that I remember showed that
solid spheres roll faster down the same slope than solid disks, which
in turn roll faster than hoops--nothing about whether a denser hoop
rolls faster, slower, or the same speed down a hill as lighter hoop.

Make sure you get the parameters of the thought experiment clear
before you lay your money down, though...

On 29 Mar 2007 22:49:14 -0700, "Ron Ruff" <[email hidden]>

Quoted message said:

Quoted message said:

Until I wonder if the extra energy is supplied by the extra
gravitational pull on the extra mass, so it all cancels out, and hoops
of the same dimensions (and CRR) will accelerate uniformly down a
slope in a vacuum.

Yep. Things are a lot simpler in a vacuum. The equation I used for
calculating the transient motion for a cyclist is:

a=P/Mi/V- CdA*Da*V^2/2/Mi- g*G*M/Mi- g*Crr*M/Mi

In a vacuum, and no power input, the only terms left are:

a= -g*G*M/Mi- g*Crr*M/Mi where g is gravitational acceleration, G is
the grade, M is the static mass, and Mi the inertial mass. So the
acceleration will be the same if M/Mi is the same for both.

Quoted message said:

So then I wonder if that means that a heavy enough wheel would refuse
to move at all down the slope, while a light enough wheel would reach
the speed of light. (I'm pretty sure that this logic must have a
gaping hole in it somewhere, but I'm floundering.)

They will both reach the speed of light at infinity.

Quoted message said:

I'm beginning to wonder if my friend has some famous damn experiment
up his sleeve. The only demonstration that I remember showed that
solid spheres roll faster down the same slope than solid disks, which
in turn roll faster than hoops--nothing about whether a denser hoop
rolls faster, slower, or the same speed down a hill as lighter hoop.

Make sure you get the parameters of the thought experiment clear
before you lay your money down, though...

Dear Ron,

I'm not even sure how I think I'm describing it.

But my friend's idea about same-dimension steel versus aluminum
rolling down a steady slope in a vacuum from the start seems to be
pretty close.

The same dimensions would idealize the distances and sizes, the vacuum
would remove pesky wind drag considerations, and the question would be
reduced (I think) down to heavier versus lighter hoops of the same
size rolling downhill.

You're saying (I think) that they'd accelerate from a standing start
at the same speed, just like a BB and a cannonball dropped in a
vacuum, right?

Sorry if I'm misunderstanding or confusing things.

Cheers,

Carl Fogel

Quoted message said:

On Thu, 29 Mar 2007 08:23:27 GMT, Ron Hardin <[email hidden]>

Quoted message said:

Some of the kinetic energy is in the spinning wheel, at the bottom
of the hill, so the bike itself has to be going forward slower by
that amount of energy. More mass in the rims, more energy in the
spinning wheel, and less in forward movement.

Dear Ron,

Another email from my friend just boiled the question down by
eliminating the bike and asking me to place my bet:

Two hoops of identical dimensions, one made of aluminum, the other of
steel, roll down an incline in a vacuum from a standing start.

If they were balls falling in a vacuum, it would be a tie because the
mass accelerates at the same rate, no matter how much there is of it.

Your explanation for the denser-heavier tire being slower sounds good
to me at first . . .

Until I wonder if the extra energy is supplied by the extra
gravitational pull on the extra mass, so it all cancels out, and hoops
of the same dimensions (and CRR) will accelerate uniformly down a
slope in a vacuum.

I think they will.

Two wheels with the same mass, diameter and centre of mass but different
distribution of mass is instructive. At the bottom energy is the same, so
rotational speed can't be. The wheel with the mass in the centre must have a
higher rotational speed to have the same total kinetic energy. This is what I
think Ron Hardin said.

Those two wheels have the same mass, but I don't think it matters what
that actual mass is. If I use two wheels just the same (same mass,
diameter and centre of mass, but one with the mass more in the centre)
but made of lead instead of steel, I expect the same linear and
rotational speeds at the bottom (we're in a vacuum, no tyre losses etc.
etc.).

So when it comes to the aluminium and steel rims of identical
dimensions, since they have the same mass distributions, I think they
will have the same rotational and linear speeds as each other at the
bottom of the slope.

It doesn't matter what either wheel is made of. It's the mass
distribution that makes the difference.

Another way of looking at it is to say that the force applied to the
centre of mass of each wheel scales with its mass since it's a
gravitational force (gravity applies a bigger force to more massive
things). But it's the reaction to that force at the ground that applies
a torque that turns the wheel. The force (and therefore torque) doesn't
scale with the moment of inertia of the wheel, but with its mass. So if
you increase the moment of inertia without changing the mass, the same
force will result in a slower rate of angular acceleration.

Quoted message said:

But Ron Ruff says (I think) that a heavier wheel is a little slower
down the slope in some model that he worked up, so that's two votes
from two Rons for heavier being slower down the slope.

Ah but Ron's heaver wheel might have also have had more of its mass
around the rim, so different mass distribution (and therefore moment of
inertia-- resistance to being spun).

Quoted message said:

So then I wonder if that means that a heavy enough wheel would refuse
to move at all down the slope, while a light enough wheel would reach
the speed of light. (I'm pretty sure that this logic must have a
gaping hole in it somewhere, but I'm floundering.)

When you approach the speed of light relativistic effects start to
become significant, and the mass increases, or something. This is why
it's so hard to develop a warp drive.

If the light wheel had the mass of a photon (very low, almost nothing) I
expect it might approach the speed of light. But in that case it
couldn't be made of aluminium or steel since a single atom of either
requires more material than a photon.

The heavy wheel will always move in the idealized situation. A flea can
move a space station, you will just get a very slow acceleration.
There's no static friction threshold to be overcome, and neither is
there in our wheel rolling experiment (although there does have to be
friction or the wheels wouldn't roll).

Orin said:

Quoted message said:

A friend was looking at the current thread about standing-start
downhill coasting tests.

He asked me whether the mass of the tires would make a difference.

I cleverly replied, "Huh?"

He expanded his question to something like this:

Given the same CRR and wind drag, will a wheel with more mass on its
rim (heavier tire) coast downhill from a standing start faster,
slower, or the same as the less massive wheel?

I cleverly replied, "Er . . ."

I'm hoping that RBT posters who like physics and equations involving
rotating masses will help me flesh out my answer.

Do the light and heavy tire behave the same way as a BB and a bowling
ball, which fall at the same speed in a vacuum?

Or do the miserable things accelerate differently because of the
rotation involved?

Heavier tire will be slower. The limiting cases are solid cylinder:
forward speed is 1.15*sqrt(g*h) and hollow cylinder: forward speed is
sqrt(g*h) where g is the acceleration due to gravity and h is the
height of the hill. The heavier the tire, the closer you are to the
hollow cylinder case and the lower the speed.

Formulae are straight from a physics text book.

Orin.

Dear Orin,

I just replied to Ron Ruff's latest post, where he says (I think) that
the heavy and light tire will roll the same--but only if everything is
idealized into hoops, which aren't really the same as wheels.

I may be describing things poorly, so bear with me.

My friend's later example is a pair of hoops of identical dimensions,
one of steel, one of aluminum, rolling down a slope in a vacuum.

If each hoop is made of a 1 inch thick rod bent into a circle 28
inches high, then I think that they both are the same in that neither
approaches a hollow cylinder more closely, whether the rod is made of
dense steel or light aluminum. And Ron Ruff is saying that they'll
roll downhill at the same speed.

But wheels with hubs ain't the same as hoops--my friend's example is
actually a different thing.

You're saying (I think) here's a wheel (not a hoop with an empty
center) with a hub, spokes, rim, and tire.

The mass is distributed outward from the hub in the form of the hub
(center), spokes (middle), rim (close to edge), and tire (very edge).

The more mass added to the tire, the closer the whole real wheel looks
to the slow-rolling hollow cylinder with the mass concentrated at the
outer edge.

So you're explaining what the two Rons were telling me earlier about a
real wheel--heavier is a little slower.

But Ron Ruff's later explanation handles hoops with empty centers. If
their dimensions are the same, then their mass is distributed the same
way, no matter what they're made of, and they roll at the same rate.

Does this distinction between real wheels and idealized hoops make
sense?

(If it does, I get to tell my friend that his stinking improved
example with the steel and aluminum hoops was entirely different and
not like real bicycle wheels at all, nyah-nyah-nyah!)

Cheers,

Carl Fogel

Quoted message said:

You're saying (I think) that they'd accelerate from a standing start
at the same speed, just like a BB and a cannonball dropped in a
vacuum, right?

Yes, *any* object that can be idealized to have all of it's mass at
the outer edge, will roll downhill at the same speed (same
acceleration). The "hoops" can have any diameter or mass. In this case
the inertial mass is always double the static mass... ie M/Mi =.5

Quoted message said:

(If it does, I get to tell my friend that his stinking improved
example with the steel and aluminum hoops was entirely different and
not like real bicycle wheels at all, nyah-nyah-nyah!)

Looks that way to me... On a bike, if you increase the hoop weight
then both the inertial and static masses go up by the same amount, but
the ratio for the whole system, M/Mi goes down... so the rate of
acceleration also drops.

Quoted message said:

Orin said:

Quoted message said:

A friend was looking at the current thread about standing-start
downhill coasting tests.

Quoted message said:

Quoted message said:

He asked me whether the mass of the tires would make a difference.

Quoted message said:

Quoted message said:

I cleverly replied, "Huh?"

Quoted message said:

Quoted message said:

He expanded his question to something like this:

Quoted message said:

Quoted message said:

Given the same CRR and wind drag, will a wheel with more mass on its
rim (heavier tire) coast downhill from a standing start faster,
slower, or the same as the less massive wheel?

Quoted message said:

Quoted message said:

I cleverly replied, "Er . . ."

Quoted message said:

Quoted message said:

I'm hoping that RBT posters who like physics and equations involving
rotating masses will help me flesh out my answer.

Quoted message said:

Quoted message said:

Do the light and heavy tire behave the same way as a BB and a bowling
ball, which fall at the same speed in a vacuum?

Quoted message said:

Quoted message said:

Or do the miserable things accelerate differently because of the
rotation involved?

Quoted message said:

Heavier tire will be slower. The limiting cases are solid cylinder:
forward speed is 1.15*sqrt(g*h) and hollow cylinder: forward speed is
sqrt(g*h) where g is the acceleration due to gravity and h is the
height of the hill. The heavier the tire, the closer you are to the
hollow cylinder case and the lower the speed.

Quoted message said:

Formulae are straight from a physics text book.

Quoted message said:

Orin.

Dear Orin,

I just replied to Ron Ruff's latest post, where he says (I think) that
the heavy and light tire will roll the same--but only if everything is
idealized into hoops, which aren't really the same as wheels.

I may be describing things poorly, so bear with me.

My friend's later example is a pair of hoops of identical dimensions,
one of steel, one of aluminum, rolling down a slope in a vacuum.

If each hoop is made of a 1 inch thick rod bent into a circle 28
inches high, then I think that they both are the same in that neither
approaches a hollow cylinder more closely, whether the rod is made of
dense steel or light aluminum. And Ron Ruff is saying that they'll
roll downhill at the same speed.

But wheels with hubs ain't the same as hoops--my friend's example is
actually a different thing.

You're saying (I think) here's a wheel (not a hoop with an empty
center) with a hub, spokes, rim, and tire.

The mass is distributed outward from the hub in the form of the hub
(center), spokes (middle), rim (close to edge), and tire (very edge).

The more mass added to the tire, the closer the whole real wheel looks
to the slow-rolling hollow cylinder with the mass concentrated at the
outer edge.

So you're explaining what the two Rons were telling me earlier about a
real wheel--heavier is a little slower.

But Ron Ruff's later explanation handles hoops with empty centers. If
their dimensions are the same, then their mass is distributed the same
way, no matter what they're made of, and they roll at the same rate.

Does this distinction between real wheels and idealized hoops make
sense?

Yes. It all depends on the distribution of the mass. The mass itself
cancels out of the equations.

Orin.

<[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

A friend was looking at the current thread about standing-start
downhill coasting tests.

He asked me whether the mass of the tires would make a difference.

I cleverly replied, "Huh?"

He expanded his question to something like this:

Given the same CRR and wind drag, will a wheel with more mass on its
rim (heavier tire) coast downhill from a standing start faster,
slower, or the same as the less massive wheel?

Same.

M = 6 kg and 12 kg
All the weight is at the rim circumference.
Starting height is 10m
Calculate V at bottom of hill

PE = mgh = 588.6 J and 1177.2 J
KE = ½ mV^2 + ½ mV^2 = 588.6 and 1177.2 (rotational and translational)
V^2 = 588.6/6 and 1177.2/12
V = Sqrt (588.6/6) V = Sqrt (1177.2/12)

V = 9.904m/s V = 9.904m/s

Phil H

extra cheese?

http://images.google.com/imgres?imgurl=http://lisa.nasa.gov/gallery/images/stellar-mass-black-hole.jpg&imgrefurl=http://lisa.nasa.gov/gallery/stellar-mass-black-hole.html&h=450&w=450&sz=9&hl=en&start=3&tbnid=uXX2tp5O8zwhsM:&tbnh=127&tbnw=127&prev=/images%3Fq%3Dblack%2Bhole%26svnum%3D10%26hl%3Den%26rlz%3D1T4DKUS_enUS211US211

http://teachertech.rice.edu/Participants/louviere/Newton/hotwheels.html