if i could run faster than the speed of light...

[Intoelectrics]

but what has this relativity theory changed? the earth still orbits the sun, along with other lumps composed of various substances, there's no definite proof that aliens have visited, the moon is still made of cheese, and if the earth stopped rotating, we'd all be flung into outer space.

More than most realize, people go about their daily lives unaware that without the understanding of Einstein's theory of relativity much of the technology we rely on would not be possible.

I often suspect there are aliens among us, you only have to look at Donald Trump and Simon Cowel

Actually the Earth's rotation makes us weigh slightly less than we would if it didn't spin, centrifugal force lifting us off the surface of the Earth. We would be slung into space if the Earth lost its gravity.

 

[Darkwood]

I figured you would know this already, (my apologies for miss interpreting your post) its obvious you know are passionate about this subject. My post wasn't intended as a criticism of your post but rather just to point out to those who don't know much about Einstein that it is a miss-conception that he was hopeless at math.

No apologies needed, I made an ambiguous comment tbh so should have worded it better, yes you are correct about the misconception and probably down to people like myself posting ambiguous comments .

 

[marconi]

Re #76 - Actually the Earth's rotation makes us weigh slightly less than we would if it didn't spin, centrifugal force lifting us off the surface of the Earth.

You might want to think again on what you wrote above, remembering that the weight W of an object with mass m in the Earth's gravitational field is W= G Mm/rsquared

where M is the mass of the earth, G the Gravitational constant and r is distance between the centres of mass of M and m..

 

[Darkwood]

@marconi
He is actually correct but the spin of the earth is so slow relative to its size that we couldn't perceive it, at the equator the effect would be 0.35% diminishing the further away from the equator you ventured.
Your formula is correct but is only applicable if other forces are not acting on the subject matter, the rotation of the earth does in fact counter the gravitational effect of the earth at the equator and is why it has a bulge of approx 20miles but on the scale of things this is not much. We do not account for inertia when calculating gravity on earth as it is most of the time too small to be relevant.

 

[marconi]

Centrifugal forces do not exist. Think on the centripetal force acting an a mass m rotating about the centre of mass of the Earth M in an orbit of radius r.

 

[Darkwood]

You highlighted the 'makes us weigh less' not the term 'centrifugal', yes if you want to get to the nitty gritty then yes centrifugal force is a pseudo force but that does not mean it cannot be used to describe an effect as it still has valid meaning if used in the right context, it is merely a simplified way to express an effect in this case of a spinning object.
So are you arguing the relevance of the word 'centrifugal' which is not what was highlighted or that it was stated one would weigh less due to the rotation of the earth relative to that of a stationary earth?
You present a formula which for all intent and purposes give enough accuracy for most applications but it is a mean average approximation, the earth is not a sphere and mass distribution is not entirely equal either, we live on an oblate spheroid and if we were to calculate the weight of an object to a high precision then we would bring in many other calculations into the equation that effect weight, now yes I am been picky here as we are talking high precision not normally needed but rotational speed of the mass creating the gravity would be factored in as it does in deed effect the end result which is the weight of an object under its influence.

I'm a little confused from which angle you are coming in from so genuinely interested.

If all the other constants remained the same hypothetically (which they wouldn't) and you stopped the earth then compared to the rotating earth the gravitational force would be 0.034m/s additional (yes I had to look it up ).. this would make you fractionally heavier in comparison which is the crooks of the matter Intoelectrics was making and myself in my responses.

 

[Intoelectrics]

You highlighted the 'makes us weigh less' not the term 'centrifugal', yes if you want to get to the nitty gritty then yes centrifugal force is a pseudo force but that does not mean it cannot be used to describe an effect as it still has valid meaning if used in the right context, it is merely a simplified way to express an effect in this case of a spinning object.
So are you arguing the relevance of the word 'centrifugal' which is not what was highlighted or that it was stated one would weigh less due to the rotation of the earth relative to that of a stationary earth?
You present a formula which for all intent and purposes give enough accuracy for most applications but it is a mean average approximation, the earth is not a sphere and mass distribution is not entirely equal either, we live on an oblate spheroid and if we were to calculate the weight of an object to a high precision then we would bring in many other calculations into the equation that effect weight, now yes I am been picky here as we are talking high precision not normally needed but rotational speed of the mass creating the gravity would be factored in as it does in deed effect the end result which is the weight of an object under its influence.

I'm a little confused from which angle you are coming in from so genuinely interested.

If all the other constants remained the same hypothetically (which they wouldn't) and you stopped the earth then compared to the rotating earth the gravitational force would be 0.034m/s additional (yes I had to look it up ).. this would make you fractionally heavier in comparison which is the crooks of the matter Intoelectrics was making and myself in my responses.

I was just about to reply to marconi. But you summed up my thoughts with this post.

Just to be clear to folk reading this thread. My initial response was a few casual remarks to telectrix's post, part of which was tongue in cheek.

But the general facts were accurate enough. The devil is in the detail we all know this and as darkwood explained in his excellent post, if we want to get really technical things can get very complicated and then many factors have to be considered.

 

[Intoelectrics]

Re #76 - Actually the Earth's rotation makes us weigh slightly less than we would if it didn't spin, centrifugal force lifting us off the surface of the Earth.

You might want to think again on what you wrote above, remembering that the weight W of an object with mass m in the Earth's gravitational field is W= G Mm/rsquared

where M is the mass of the earth, G the Gravitational constant and r is distance between the centres of mass of M and m..

I'm very aware of this, but does not account for inertia.
My initial response was to telectrix post where he said "if the earth stops rotating we will all be flung off" . I took it as a flippant statement and a bit of fun to which I responded with an equally flippant post and a bit of fun.

 

[telectrix]

there's also the gravitational pull of the sun and the moon to be taken into account. after all, they pull millions of gallons of seawater up to about 30 ft.

 

[Intoelectrics]

there's also the gravitational pull of the sun and the moon to be taken into account. after all, they pull millions of gallons of seawater up to about 30 ft.

Absolutely, there are many factors to consider when we talk about changing the conditions by even a small amount. Depends how deep you wanna go with it

 

[telectrix]

I'm very aware of this, but does not account for inertia.
My initial response was to telectrix post where he said "if the earth stops rotating we will all be flung off" . I took it as a flippant statement and a bit of fun to which I responded with an equally flippant post and a bit of fun.

it was maybe flippant, but consider.. due to the earth's rotation, we are travellin in space at approx. 1000 mph although relative to the earth stationary. now if the earth suddenly stopped 9 akin to the car you are in hitting a solid immoveable mass of concrete) you'd still be travelling at 1000 mph and so your body would continue, and be thrown off untill such time as air friction slowed you down enough for gravity to take over and you'd be roughly deposited in Tokyo.or even worse, America, ultimately, dependent on your aerodynamics, you could end up where you started but yesterday..

 

[Darkwood]

@telectrix ... theoretically stopping the world would be mass extinction event, the g force would wipe out nearly all life instantly near the equator, the atmospheric mass would initially see winds of 1000mph at the equator slowing down as ground resistance and air drag acted on it then we got all the secondary effects miles high tsunamis, massive earthquakes, mega volcanic eruption etc, tbh getting your insides turned inside out by the initial G force would be a blessing considering what came after... can't think of a silver lining tbh well except Justin Beiber would also be out of the equation.

 

[marconi]

This is what I am addressing: Actually the Earth's rotation makes us weigh slightly less than we would if it didn't spin, centrifugal force lifting us off the surface of the Earth. We would be slung into space if the Earth lost its gravity.


What I am discussing with you is the statement the OP made that the force acting on 'us' or mass m decreases because the earth of mass M is rotating about its axis once a day. Taking the statement further, it means that as the rate of rotation of the Earth increases more and more then the weight of us (mass m) decreases further and further until eventually the force is very small or zero. The gravitational interaction force is always a pull not a push so in the spherical context of the earth and us the force is centripetal meaning moving or tending to move towards a centre - M and m are being pulled to be together. The centripetal force never becomes negative or acting to push M and m apart viz a centrifugal force.

The force of gravity between M and m is a force of interaction. The pull M exerts on m is exactly the same as the pull m exerts on M. This force is what is commonly called the weight of the object and it depends on the size of the two masses and their distance apart according to;

W is proportional to M x m/rsquared.

So the closer the objects are together the stronger the force. And the bigger product of their respective masses the greater is the force they exert on each other. The direction of this force is along the straight line which joins the masses. This means that any acceleration of m or M will be along this line too. Nowhere in this is there an angular velocity term to describe the physics suggested by the OP in mathematics that the force of interaction is a function of M, m, r and Q(the rate of rotation of the Earth about its North-South axis).

We now consider the application of the OPs statement to a man (m) standing on the earth; let us say at the equator. He is not moving relative to the surface of the earth but he is moving in an orbit whose axis is North-South. He completes one revolution every 24 hour. Knowing the radius of the Earth at the equator where is is standing one can work out his orbital speed as V = Q x 2 x pi x r. Even though it seems to him he is stationary he is actually following a circular path. Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion. The change of direction is perpendicular to its orbital path - that is in the radial direction. This constant change of direction is an acceleration - a centripetal acceleration.

The centripetal acceleration A = Vsquared/r

Mass m has this centripetal acceleration because there is a centripetal force which causes it. This centripetal force is the resultant force or net force acting on mass m.

So what are the forces acting on the man m standing stationary on the equator? As mentioned before there is his weight W. If this was the only force then the man would accelerate and move at increasing speed towards the centre of mass of the Earth. He does not move radially because the earth beneath him is solid and so the earth provides a force of reaction U equal and opposite to his weight which is upwards. If the Earth was not spinning then W - U = 0.

But the earth is spinning and the man m is experiencing a radial or centripetal acceleration A. So, the resultant force on M is W - U = A. For constant masses M and m, and constant radius r, the weight W is constant. Thus, the force of reaction U reduces when the man m is rotating about the N-S axis. If the Earth spun faster he would 'feel lighter' ie less upwards force on the soles of his feet but his weight and the force W remain unchanged. If he was to run in the direction of rotation of the earth around the equator ie have some speed relative to the earth, he could only do this if U decreased further - so the faster he goes the lighter he feels. If he was to run in the opposite direction to the spinning earth then U would increase (he would start to feel heavier) until he was stationary in space. Any further increase in pace from then on in this counter direction would result in U decreasing again and him feeling lighter (but NOT WEIGHING LESS).

 

[Darkwood]

@marconi - You didn't get the context it was written in or my reply to yours, I/we are not disagreeing with you just pointing out from the position it was written, I fully understand and agree with every word you have written except the last point which I'll come back to, you are approaching the subject from the opposite side and I am trying to explain that even though centrifugal force is a pseudo science it is still commonly used in applied physics to represent the effect you go deeper into .
When measuring a fixed mass like weighing yourself that is subject to other forces like been on a roller coaster or in a lift your weight will increase or decrease in correlation to the acceleration or decelerating forces you are subject to while your mass remains fixed we acknowledge this as a change in weight, all you have done is broken down the difference in weight and mass to its core values and explained which acting forces are changing and why, this still does not change what is happening in that we are getting lighter of heavier as a result of various forces acting on our mass, the term weight is the outcome of the forces acting on your mass relative to a fixed frame reference, this is why I disagree only with your final point in that you say 'feeling' lighter , no this in my opinion is a wrong statement to make although I understand why you say it and in the right context it would be a valuable point but for our discussion weight does change and is measurable therefore our perception of weight has changed and is true, explaining what causes that change does not change what weight is and how we perceive it.

PS enjoyable debate btw

 

[telectrix]

way above my head this, but you've still not proved that the earth is not flat.