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When an object moves at light speed it stretches out to the eye of the observer.

When an object moves at light speed it stretches out to the eye of the observer. So what happens when an object follows a circular path at light speed. e.g. a windmill spinning at the speed of light?C

Quote from: chris on 11/09/2015 08:23:57When an object moves at light speed it stretches out to the eye of the observer. So what happens when an object follows a circular path at light speed. e.g. a windmill spinning at the speed of light?CIn my opinion based on observations there are such cases in reality...

In my opinion based on observations there are such cases in reality...

In order to move in a circle, the object must be subject to a centripetal force.Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion

If you could whirl a significant mass at relativistic speeds, it would radiate energy in the form of gravitational waves (or so the theory of general relativity and confirming astronomical measurements indicate).

Quote from: alancalverd on 11/09/2015 09:16:18In order to move in a circle, the object must be subject to a centripetal force.Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion Which equation are you using here?--lightarrow

Quote from: lightarrow on 12/09/2015 11:44:15Quote from: alancalverd on 11/09/2015 09:16:18In order to move in a circle, the object must be subject to a centripetal force.Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion Which equation are you using here?--lightarrowm = m_{0}/√{1-v^{2}/c^{2}} is good enough for CERN and me.

The centripetal force required to maintain circular motion of a body moving at relativistic speeds is F = γm_{0}v^{2}/rwhere v is the instantaneous tangential velocity.

Any force will do if you wait long enough - the principle behind solar sails and ion rockets.The problem is that "long enough" is infinite, whatever the force applied, if you want a massive particle to reach c. How is that "interesting"?

We're not talking about "relativistic speeds" but c.

The centripetal force required to maintain circular motion of a body moving at relativistic speeds isF = γm_{0}v^{2}/rwhere v is the instantaneous tangential velocity

Accelerating leptons to 0.99c in a circular path is an engineering problem, but the physics is no big deal. It's the recurring decimal point that distinguishes between difficult and impossible. Your equation is awaited with bated breath.

Since a massive object will have infinite mass at c

]We're not talking about "relativistic speeds" but c.

A relativistic speed is a speed which is a significant proportion of the speed of light.

m_{v} = m_{0}(1 - v^{2}/c^{2})^{−1/2}This works for "relativistic speeds" but clearly raises problems when v = c, as Einstein remarked. And who am I to disagree?

Pretty much the same as the difference between "green-ish" and "λ = 520 nm". 0.99c is a relativistic speed in most people's language. c is c.

The point is that all and only photons travel at c, whereas any particle with nonzero mass could in principle travel at any speed less than c. That makes c rather special, and 0.999c rather ordinary.

what happens when an object follows a circular path at light speed?

what did you mean when you wrote "We're not talking about "relativistic speeds" but c."?

Your problem is the obstination to want to use equations which are valid only for velocities different from c. If you used those which are always valid, for all velocities included c, you wouldn't need to "climb on the mirrors" []--lightarrow

Tangential force. In modulus: F = (E/r)*β^{2}E = energy.β = v/cFor a body with mass: E = mc^{2}γ; γ = (1-β^{2})^{-1/2}For a body moving at c: β = 1.About the energy needed to accelerate a body to light speed, see "E" up. For a photon you can write E = h*f if you like.--lightarrow

If we take the value we end up with . How do you come to this determination? Beta may equal 1 according to your previous post but then you are taking the square root of zero and dividing it into 1. How is that valid? None of this has a bearing upon c.

Tangential force. In modulus: F = (E/r)*β^{2}E = energy.β = v/cFor a body with mass: E = mc^{2}γ; γ = (1-β^{2})^{-1/2}For a body moving at c: β = 1.

Quote from: lightarrow on 16/09/2015 16:08:38Tangential force. In modulus: F = (E/r)*β^{2}E = energy.β = v/cFor a body with mass: E = mc^{2}γ; γ = (1-β^{2})^{-1/2}For a body moving at c: β = 1.Agreed, so as v→c, E → ∞ if m ≠ 0And the radial force required to maintain circular motion of a massive body at v = c is?

Quote from: lightarrow on 16/09/2015 16:08:38Tangential force. In modulus: F = (E/r)*β^{2}E = energy.β = v/cFor a body with mass: E = mc^{2}γ; γ = (1-β^{2})^{-1/2}For a body moving at c: β = 1.About the energy needed to accelerate a body to light speed, see "E" up. For a photon you can write E = h*f if you like.--lightarrowDid you know that in his 1905 paper on special relativity Einstein got the expression for the transverse mass wrong? Ohanian explains the error in his book Einstein's Mistakes located at ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN

Ehm, I wrongly wrote "tangential" force but it clearly was "radial" force. Sorry for the mistake and thank you to have noticed it!I am correcting it.--lightarrow