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   sci.physics.relativity      The theory of relativity      225,861 messages   

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   Message 225,383 of 225,861   
   Paul B. Andersen to All   
   Re: Galaxies don't fly apart because the   
   24 Jan 26 12:34:33   
   
   From: relativity@paulba.no   
      
   Den 24.01.2026 07:51, skrev Maciej Woźniak:   
   > On 1/23/2026 8:32 PM, Paul B. Andersen wrote:   
   >> Den 22.01.2026 22:31, skrev Maciej Woźniak:   
   >>> On 1/22/2026 9:57 PM, Paul B. Andersen wrote:   
   >>>> Den 21.01.2026 16:11, skrev Maciej Woźniak:   
   >>>>> On 1/21/2026 3:31 PM, Paul B. Andersen wrote:   
   >>>>>>   
   >>>>>> You are swinging an object around you in a string.   
   >>>>>> Is the object accelerating towards you, or away   
   >>>>>> from you? Or is it not accelerating at all?   
   >>>>>   
   >>>>> Towards me.   
   >>>>   
   >>>> Right, well done.   
   >>>>   
   >>>> So you have understood that the object is accelerating   
   >>>> in the direction the force acting on it is pulling it.   
   >>>> This direction is along the string towards your hand.   
   >>>> The acceleration is:   
   >>>>    a = F/m   
   >>>> where F is the tension in the string and m is the mass   
   >>>> of the object.   
   >>>>   
   >>>> Let us look at a concrete example.   
   >>>> The length of the string is L = 1.4142 m, and the mass m is 1 kg.   
   >>>> You swing the object such that it takes t = two seconds to make   
   >>>> a full turn.   
   >>>> You observe that the angle of the string to the ground is 45⁰.   
   >>>> That means that the radius of the circle the object is moving   
   >>>> along is:   
   >>>>   r = L/√(2) = 1 m   
   >>>> It is then easy to calculate that the speed of the object is   
   >>>>   v = 2⋅π⋅r/t = 3.14 m/s   
   >>>> The horizontal centripetal acceleration is:   
   >>>>   aₕ = v²/r = 9.8 m/s²  (towards centre of circle)   
   >>>> The horizontal component of the tension in the string is:   
   >>>>   Fₕ = m⋅aₕ = 9.8 N   
   >>   
   >> The horizontal component of the force acting on the object is:   
   >>    Fₕ = 9.8 N  (constant towards centre of circle))   
   >>   
   >>>> Since the angle of the string to the ground is 45⁰, the vertical   
   >>>> component of of the tension in the string is:   
   >>>>   Fᵥ = Fₕ   
   >>   
   >> The vertical component of the force acting on the object is:   
   >>    Fᵥ = 9.8 N  (constant upwards)   
   >   
   > So what?   
      
   Do you have a reading comprehension problem?   
      
   So according to Newton's law F = ma the acceleration   
   of the object is a = F/m = 9.8 m/s²  (upwards)   
      
   >The vertical component of the velocity   
   > remains constant and 0. No vertical acceleration,   
   > sorry, poor trash.   
      
   I see. You think that if an object is stationary   
   in its rest frame, then its acceleration must be zero.   
      
   :-D   
      
   --   
   Paul   
      
   https://paulba.no/   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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