3. In polar coordinates the position of a point-particle is described by the vector = rr(0),...

 

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§3. In polar coordinates the position of a point-particle is described by the vector = rr(0), where r = = r(t) is the radial coordinate, (0) is a unit vector in the radial direction, 0 = e(t). The parameter t represents time. Knowing that d do v= -= Ô, dô do =-^, where is a unit vector in the angular direction, use the chain rule to show that the velocity and acceleration vectors are, respectively, d d dt r = r'î+ro'Ô, ā= -= dt (r" −r0¹²)î+(r0″+2r′0′)Ô. Notation: the prime denotes a derivative with respect to time. Remark: v₁ = r' is the tangencial velocity; v = re' is the angular velocity; a = r0¹² is the centripetal acceleration; ac = 2r'0' is the coriolis acceleration. §3. In polar coordinates the position of a point-particle is described by the vector = rr(0), where r = = r(t) is the radial coordinate, (0) is a unit vector in the radial direction, 0 = e(t). The parameter t represents time. Knowing that d do v= -= Ô, dô do =-^, where is a unit vector in the angular direction, use the chain rule to show that the velocity and acceleration vectors are, respectively, d d dt r = r'î+ro'Ô, ā= -= dt (r" −r0¹²)î+(r0″+2r′0′)Ô. Notation: the prime denotes a derivative with respect to time. Remark: v₁ = r' is the tangencial velocity; v = re' is the angular velocity; a = r0¹² is the centripetal acceleration; ac = 2r'0' is the coriolis acceleration.