From: relativity@paulba.no   
      
   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.   
      
   >>   
   >> I bet you [Maciej Woźniak] won't give a sensible answer.   
   >> You never do.   
      
   I was wrong about that.   
   You gave a very sensible answer.   
      
   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   
   Since the angle of the string to the ground is 45⁰, the vertical   
   component of of the tension in the string is:   
      Fᵥ = Fₕ   
   So the vertical acceleration is:   
      aᵥ = Fᵥ/m = 9.8 m/s²  (upwards)   
   The tension i the string is:   
      F = √(Fₕ² + Fᵥ²) = 13.86 N   
   And the acceleration of the object is:   
      a = F/m = 13.86 m/s² (towards your hand)   
      
   I am sure you will understand this, and   
   will give a sensible response.   
      
   --   
   Paul   
      
   https://paulba.no/   
      
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