Can anyone explain this? I'm standing in the middle ........?

Question

Im standing in the middle of the U.S. I have a harness around my waist with a featherlight pipe with a ball on the end which extends to New York City. I spin around in a circle which takes 2 seconds........this means, the ball on the end flew over Canada, whizzed over California, blazed over Mexico, and returned to New York City in 2 seconds. Can you explain this?

My question has nothing to do with the speed of light.......its the fact that it seems that all you have to do is spin around, yet you can make an object ( the ball ) travel at such a high speed, it doesn't seem possible, but if you can just spin around, it is! Crazy.

Answer 1

Allow me to add a few more specifics, if I understand your question correctly....We're already assuming that the mass of the rod is negligible; let's also, in addition, assume that the whole system of you, the rod, and the rotating mass is perfectly rigid.

That said, I think you are forgetting Newton's second law: force equals mass times acceleration.

F = m*a

In order to accelerate the mass at the end of the pole, in such a way that it makes the "round" trip of around 12,400 km in two seconds flat, it is going to take a rather large amount of force......

How much force, you may ask?

That depends on the mass and the acceleration. Lets say that the mass at the end of your ephemeral pole has the mass of a grain of sand, ( around 10 milligrams, or 10^-5 kg.) Lets also assume that you spend you spend your entire two seconds accelerating the sand grain forward at a constant rate, and at the end, it comes crashing into a brick wall...(just to make things interesting...) By these assumptions, at the end of it's journey the sand grain has reached a convenient velocity of 12,400,000 m/s.

Now I'm ready to calculate the force. at the end of the trip, the sand grain has the momentum of:

P = m*v = 1,240 kgm/s,

(which is roughly equivalent to being hit by 10 linebackers at once...) And since momentum also equals force multiplied by time (assuming the force is constant:)

P = F*t

F = P/t

Then, dividing by two seconds gives a force of 610 newtons, or about 137 lbs.

OK, that sounds reasonable, even for accelerating a grain of sand, but hold on for a second! That's the force that the grain of sand is feeling at the *end* of a 1,970 km long pole! Since you are whipping that pole in a circle, you are not strictly applying a *force* to the pole, but a *torque*......Again, simple physics comes to the rescue; torque being equal to force times distance....

T = F*d.

This equals around 1,201,700 Nm of torque, an amount so huge, that it pretty much destroys any credibility that is left in this whole thought experiment......;-) It's not humanly possible...

So, in conclusion, you are certainly welcome to *try* to spin this grain of sand through 12,400 km, in two seconds, but you probably just don't have what it takes.......

Hope I haven't wasted too much time.....
~W.O.M.B.A.T.

Answer 2

To put it simply, both you and the ball at the end of the pipe have the same angular velocity but different linear velocities. You're both covering the same amount of a circle in the same time, as measured in radians per second. However, since the "outer" circle is so much larger, covering the same proportion of the circle requires a much higher linear velocity as measured in meters per second. Hope this helps.

Edit-
And the people talking about the speed of light really need to run the numbers before running their mouths. The diameter of the US is 3000 miles. Multiply by pi to get 9420 miles traveled by the ball. Divide by 2 seconds to get 4710 miles/second. Which is only 2.5% light speed (186,000 miles/second). It's fast, but barely fast enough to even notice time dilation. If you could complete your turn in 0.05 seconds you might have something to worry about.

Answer 3

What is there to explain? torque, rotational inertia, acceleration? This is hypothetical because you will never have a pole that long(probly about 13-15 hundred miles) and it would not be light enough to hold. So hypothetically if you could do that then yes you could move a tennis ball from new york to california in 1 second. and back to new york.

What would that accomplish? Now if it were made into a transportation device it would be useful. But that is not practical.

Answer 4

Ball will never reach your speed. There always will be a lag. Just like arms of spiral galaxies. Core of galaxies rotate rapidly although the arm rotates very slowly.
Longer your rod is, greater will be the lag.
In fact you can do that experiment in your neighborhood park by tying a heavy object with a rope, hold its other end and spin. Longer the rope, greater would be the lag of that object. In fact at the end, you will end up with the rope wrapped around your body (because of the lag)

Answer 5

You can't do that. No matter how light are the pipe and the ball, as the speed gets close to the speed of light, the mass increases until it's impossible for you to keep moving.

Answer 6

If your question has to do with the speed of light, then, no, the ball wouldn't ever reach the tiniest fraction of the speed of light.

Light travels at 186,282.397 *miles* per *second*

So your ball could make that trip about 23,000 times per second.

But to answer your question more directly, no, I can't explain how you'd do that; I only know that you wouldn't need to consider the speed of light in your calculations.

Answer 7

You turned around in two seconds but the ball and featherlight rod cought air resistence and hit a hole bunch of buildings and never cought up with you causing it to never reach you till 2 minutes later. lol

Answer 8

You have described a circle that covers almost all of the continental US, parts of canada, and part of mexico. They probably want you to calculate the velocity of the ball

Answer 9

Must be a very stiff pipe. What's the question?

Answer 10

Sure.
The pipe with a ball on the end is a bong, you are high on drugs.