username459260
Badges: 16
Rep:
?
#1
Report Thread starter 7 years ago
#1
Before I present the question I would like you to make two assumptions:
1) no other planetary body affects the centre of mass of the earth
2) the mass of the earth and hula-hoop is uniformly distributed

Question:
If you were to take an enormous hula-hoop (whose diameter is larger than the diameter of the earth) and place it such that its centre of mass appears at EXACTLY the same point as the earths centre of mass AND it lies PERFECLY over the equator would the hula-hoop float above the earth? (imagine a ball surrounded by a small ring - the ring does not touch the ball and the ring lies perfectly over the equator of the ball)

I believe it would because the NET gravitational forces acting on the hula hoop are zero so there would be no acceleration for the hula hoop to start moving and fall
is this correct?

Question 2

Would the hula hoop start spinning around its centre of axis? why?
0
reply
Stonebridge
Badges: 13
Rep:
?
#2
Report 7 years ago
#2
You have to make a number of assumptions.
eg. The Earth is a perfect sphere with uniform density. (Only gravitational forces considered?)
1) If the mass of the Earth and the hoop are both uniformly distributed, and the hoop is placed dead centre so that the system is symmetrical, then there will indeed be no resultant force on the hoop. It would "float".
The centre of mass of the Earth and of the hoop will be at the same point.

2) Is the hoop at rest while the Earth spins under it?
If so, then why would it start to spin? To do this there would need to be a tangential force on the hoop. Where would this come from?
0
reply
Steezy
Badges: 15
Rep:
?
#3
Report 7 years ago
#3
Wow.... Good question. I can't help but will be interested to read answers...
0
reply
hecandothatfromran
Badges: 2
Rep:
?
#4
Report 7 years ago
#4
(Original post by jsmith6131)
Question 2

Would the hula hoop start spinning around its centre of axis? why?
Well, let me use mathematical terms rather than physics terms. If the hula hoop wasn't a Lamina (two dimensional shape) and a charge carrier. Then in a particular orientation it would indeed spin because the earth does indeed have a non-negligible magnetic field.

If the hula hoop was placed with it's plane face parallel to the direction of the magnetic field, then it spin with the direction of motion perpendicular to the plane of face of the hula hoop. Can you think and explain why?
0
reply
Stonebridge
Badges: 13
Rep:
?
#5
Report 7 years ago
#5
(Original post by hecandothatfromran)
Well, let me use mathematical terms rather than physics terms. If the hula hoop wasn't a Lamina (two dimensional shape) and a charge carrier. Then in a particular orientation it would indeed spin because the earth does indeed have a non-negligible magnetic field.

If the hula hoop was placed with it's plane face parallel to the direction of the magnetic field, then it spin with the direction of motion perpendicular to the plane of face of the hula hoop. Can you think and explain why?
So it's hoop made of ferrous metal?
They are normally made of plastic and would not respond to magnetic fields.
You need to state what assumptions you are making.
0
reply
hecandothatfromran
Badges: 2
Rep:
?
#6
Report 7 years ago
#6
(Original post by Stonebridge)
So it's hoop made of ferrous metal?
They are normally made of plastic and would not respond to magnetic fields.
You need to state what assumptions you are making.
Nah, just a charge carrier. As the earth rotates, there's relative motion and hence a current is induced (follows from faraday's law)? that works, right?
0
reply
Stonebridge
Badges: 13
Rep:
?
#7
Report 7 years ago
#7
(Original post by hecandothatfromran)
Nah, just a charge carrier. As the earth rotates, there's relative motion and hence a current is induced (follows from faraday's law)? that works, right?
OK. So it's a metal hoop.
Yes. It's possible there could be currents induced in it due to the Earth's magnetic field.
So you're saying these currents would provide a magnetic field that would interact with the Earth's field. Right?

Certainly more fun than a plastic hoop.

I'm not sure if the OP had this in mind.
Let's wait and see.
0
reply
hecandothatfromran
Badges: 2
Rep:
?
#8
Report 7 years ago
#8
(Original post by Stonebridge)
OK. So it's a metal hoop.
Yes. It's possible there could be currents induced in it due to the Earth's magnetic field.
So you're saying these currents would provide a magnetic field that would interact with the Earth's field. Right?

Certainly more fun than a plastic hoop.

I'm not sure if the OP had this in mind.
Let's wait and see.
I know right?

Lets .
0
reply
teachercol
Badges: 9
Rep:
?
#9
Report 7 years ago
#9
Probably an unstable equilibrium ie an infinitesimal displacement would lead to it falling
0
reply
username459260
Badges: 16
Rep:
?
#10
Report Thread starter 7 years ago
#10
(Original post by teachercol)
Probably an unstable equilibrium ie an infinitesimal displacement would lead to it falling
to clarify I did not intend that the hoop would be metal but I find the concept of it being metal very interesting. thanks so much for your replies. this condo led to a long discussion between myself and my friend and I am glad we know have an answer
0
reply
Stonebridge
Badges: 13
Rep:
?
#11
Report 7 years ago
#11
(Original post by jsmith6131)
to clarify I did not intend that the hoop would be metal but I find the concept of it being metal very interesting. thanks so much for your replies. this condo led to a long discussion between myself and my friend and I am glad we know have an answer
So what was the answer? (And the justification.)

One further point to ponder.
The gravitational field strength inside a hollow sphere is zero. A ring is an element of a hollow sphere.
0
reply
teachercol
Badges: 9
Rep:
?
#12
Report 7 years ago
#12
Read Ringworld by Larry Niven for a novel set on such a ring around the Sun.
0
reply
Joinedup
Badges: 20
Rep:
?
#13
Report 7 years ago
#13
(Original post by Stonebridge)
So what was the answer? (And the justification.)

One further point to ponder.
The gravitational field strength inside a hollow sphere is zero. A ring is an element of a hollow sphere.
I was trying to explain why to someone a few weeks ago. The day after the gravitational railroad featurette on that james may tv show.

I don't think I succeeded.
0
reply
username459260
Badges: 16
Rep:
?
#14
Report Thread starter 7 years ago
#14
(Original post by Stonebridge)
So what was the answer? (And the justification.)

One further point to ponder.
The gravitational field strength inside a hollow sphere is zero. A ring is an element of a hollow sphere.
the answer was, if we follow the assumptions set out in the OP, the ring would in deed float.

I think that if a metal hoop was given an inital spin, it would continue spinning owing to the induced eddy currents
0
reply
Joinedup
Badges: 20
Rep:
?
#15
Report 7 years ago
#15
(Original post by jsmith6131)
the answer was, if we follow the assumptions set out in the OP, the ring would in deed float.

I think that if a metal hoop was given an inital spin, it would continue spinning owing to the induced eddy currents
that sounds like a perpetual motion machine.

I see two problems.
1. Metal has resistivity so inducing an eddy current in it will cause heating. The initial Kinetic energy is converted to heat.

2. Lenz law. The induced eddy currents must be in the opposite direction to the direction that would keep your hoop cutting flux.

you could make a hoop of super conductive material which wouldn't heat... But the eddy currents would be huge and the force resisting movement would also be enormous.
0
reply
username2769500
Badges: 3
Rep:
?
#16
Report 3 years ago
#16
Have they tried this? Is there really vitrified chambers and portal guns in a big empty mineshaft?
Well how did they find out the laws in the first place? If you get an answer from yourself from another dimension you'll know.
0
reply
Kyx
Badges: 6
Rep:
?
#17
Report 3 years ago
#17
(Original post by Stonebridge)
So it's hoop made of ferrous metal?
They are normally made of plastic and would not respond to magnetic fields.
You need to state what assumptions you are making.
It's a ferrous wheel!
1
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (80)
14.18%
I'm not sure (26)
4.61%
No, I'm going to stick it out for now (179)
31.74%
I have already dropped out (12)
2.13%
I'm not a current university student (267)
47.34%

Watched Threads

View All