thrown off

How fast would the earth have to spin, so that stuff
started flying off?

--
Rich

On 20/06/2013 10:28 PM, wrote:
How fast would the earth have to spin, so that stuff
started flying off?


Given the Earth's radius is 6367.5 km, a 1 kg mass, being held down by 1
N of gravitational force would need to balance out that 1 N of gravity
with an equal and opposite 1 N centripetal force, at a minimum.
Therefore the Earth would need to rotate at an incredible speed of
rotation speed of 2.523 km/s = 5645 mph = 9084 km/h at the equator!

The Earth's actual current rotational speed is only 0.4651013 km/s =
1040.4 mph = 1674.365 km/h. This results in a miniscule centripetal
force of only 0.03397 N, against the Earth's gravitational force of 1 N
on a 1 kg mass.

Yousuf Khan

Yousuf Khan wrote:
On 20/06/2013 10:28 PM, wrote:
How fast would the earth have to spin, so that stuff
started flying off?


Given the Earth's radius is 6367.5 km, a 1 kg mass, being held down
by 1 N of gravitational force would need to balance out that 1 N of
gravity with an equal and opposite 1 N centripetal force, at a
minimum. Therefore the Earth would need to rotate at an incredible
speed of rotation speed of 2.523 km/s = 5645 mph = 9084 km/h at the
equator!
The Earth's actual current rotational speed is only 0.4651013 km/s =
1040.4 mph = 1674.365 km/h. This results in a miniscule centripetal
force of only 0.03397 N, against the Earth's gravitational force of 1
N on a 1 kg mass.

Yousuf Khan

You are forgetting the Earth's gravitational acceleration in the equation!
Earth's gravitational force on a 1 kg mass is 9.8 N. g = 9.8 m/s^2.

Hence for balance, mg = m v^2/r or, circular velocity v for balance of
centripetal acceleration and gravitational attraction is v = sqrt (rg) =
7900 m/s or 7.9 km/s. For a circumference of 40000 km, the rotation period
would need to be 1.406 hours (5063 sec).

The reduction in weight at the equator vs the poles for today's 23h56m
rotation period (neglecting obliquity of the Earth) is about 0.0034 or 0.34
%.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

Mike Dworetsky wrote:
Yousuf Khan wrote:
On 20/06/2013 10:28 PM, wrote:
How fast would the earth have to spin, so that stuff
started flying off?


Given the Earth's radius is 6367.5 km, a 1 kg mass, being held down
by 1 N of gravitational force would need to balance out that 1 N of
gravity with an equal and opposite 1 N centripetal force, at a
minimum. Therefore the Earth would need to rotate at an incredible
speed of rotation speed of 2.523 km/s = 5645 mph = 9084 km/h at the
equator!
The Earth's actual current rotational speed is only 0.4651013 km/s =
1040.4 mph = 1674.365 km/h. This results in a miniscule centripetal
force of only 0.03397 N, against the Earth's gravitational force of 1
N on a 1 kg mass.

Yousuf Khan

You are forgetting the Earth's gravitational acceleration in the
equation! Earth's gravitational force on a 1 kg mass is 9.8 N. g =
9.8 m/s^2.
Hence for balance, mg = m v^2/r or, circular velocity v for balance of
centripetal acceleration and gravitational attraction is v = sqrt (rg) =
7900 m/s or 7.9 km/s. For a circumference of 40000 km, the
rotation period would need to be 1.406 hours (5063 sec).

The reduction in weight at the equator vs the poles for today's 23h56m
rotation period (neglecting obliquity of the Earth) is about 0.0034
or 0.34 %.

Thinking about it for a moment, the required speed would be the same as that
needed for reaching orbital velocity at altitude zero. If there were no
atmosphere that would work, so stuff would start "flying off", but only at
the equator.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

In article ,
"Mike Dworetsky" wrote:

snip

Thinking about it for a moment, the required speed would be the same as that
needed for reaching orbital velocity at altitude zero. If there were no
atmosphere that would work, so stuff would start "flying off", but only at
the equator.

Yes, once the linear speed of a point on the surface reaches sqrt(1/2)
times the escape velocity.

--
Odysseus

In sci.astro message , Fri, 21
Jun 2013 10:50:09, Mike Dworetsky
posted:

Mike Dworetsky wrote:
Yousuf Khan wrote:
On 20/06/2013 10:28 PM, wrote:
How fast would the earth have to spin, so that stuff
started flying off?


Thinking about it for a moment,

That is contrary to established custom; but Gandhi would have had
something to say about that.

the required speed would be the same as that needed for reaching
orbital velocity at altitude zero. If there were no atmosphere that
would work, so stuff would start "flying off", but only at the equator.


For a spherical symmetry, the period of a circular orbit depends only on
the mean density of the body within the sphere of which that circle is a
Great Circle, being given by
T^2 = (3 pi) / (G rho) .

http://www.merlyn.demon.co.uk/gravity2.htm#Gdy refers.

--
(c) John Stockton, nr London, UK. Mail via homepage. Turnpike v6.05 MIME.
Web http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms and links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.

On Thu, 20 Jun 2013 19:28:24 -0700 (PDT),
wrote:

How fast would the earth have to spin, so that stuff
started flying off?


I have a question. How much would a 200 pound person weigh if the
earth did not spin

wrote:
On Thu, 20 Jun 2013 19:28:24 -0700 (PDT),
wrote:

How fast would the earth have to spin, so that stuff
started flying off?


I have a question. How much would a 200 pound person weigh if the
earth did not spin

A 200-lb polar explorer at 90 deg latitude would weigh the same whether or
not the Earth was spinning.

At the equator the weight (measured by a spring scale) would be 0.68 kg less
than at the pole, with the Earth's current rate of spin. But the person's
mass would still be the same.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

Dear r_dela...:

On Thursday, June 20, 2013 7:28:24 PM UTC-7, wrote:
How fast would the earth have to spin, so that stuff
started flying off?

Others have given you an answer based on the Earth being a solid body with its current shape.

The Earth is like a creme filled chocolate, and if you even tried to double its speed, it would lobe up, and spin off another Moon. Even a 50% increase would be pretty disastrous.

David A. Smith

dlzc wrote:
Dear r_dela...:

On Thursday, June 20, 2013 7:28:24 PM UTC-7,
wrote:
How fast would the earth have to spin, so that stuff
started flying off?

Others have given you an answer based on the Earth being a solid body
with its current shape.

The Earth is like a creme filled chocolate, and if you even tried to
double its speed, it would lobe up, and spin off another Moon. Even
a 50% increase would be pretty disastrous.

David A. Smith

If by double its speed, you mean an equatorial velocity of 0.93 km/s, it
would have only a very small effect (slightly more oblate) and in fact the
Earth probably had such a speed a very long time ago. The idea that the
Earth "spun off" the Moon is very old and nowadays pretty well discredited.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)