4. Non-inertial frames (a) Using the chain rule, rewrite the D=2+1 Minkowski line element d-df+d +...

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4. Non-inertial frames (a) Using the chain rule, rewrite the D=2+1 Minkowski line element d-df²+d² + dy in polar coordinates: z=rcos, y=rsin 0, 1 = t. (b) Rewrite ds in a rotating frame, where the new coordinates are cos ut sinut z= Rr, i=t. coswt) The new differentials are sinut (c) Redo the previous part in polar coordinates; that is, let the new coordinates be at +6o where 6, is the old (I. r.) with the relations from part 4a but with azimuthal coordinate. (d) Consider the action for a relativistic massive particle in (D=2+1) Minkowski space =me [dr where 7 is the proper time along the worldline, ds² = -²dr². Using the action principle, derive the centripetal force experienced by a particle using uniformly rotating coordinates, 0= wt. 4. Non-inertial frames (a) Using the chain rule, rewrite the D=2+1 Minkowski line element d-df²+d² + dy in polar coordinates: z=rcos, y=rsin 0, 1 = t. (b) Rewrite ds in a rotating frame, where the new coordinates are cos ut sinut z= Rr, i=t. coswt) The new differentials are sinut (c) Redo the previous part in polar coordinates; that is, let the new coordinates be at +6o where 6, is the old (I. r.) with the relations from part 4a but with azimuthal coordinate. (d) Consider the action for a relativistic massive particle in (D=2+1) Minkowski space =me [dr where 7 is the proper time along the worldline, ds² = -²dr². Using the action principle, derive the centripetal force experienced by a particle using uniformly rotating coordinates, 0= wt.