2. Prescribed Motion and Dynamic Equation (190 points). A 6 kg collar travels along a perfectly smooth horizontal rod de

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2 Prescribed Motion And Dynamic Equation 190 Points A 6 Kg Collar Travels Along A Perfectly Smooth Horizontal Rod De 1 (17.66 KiB) Viewed 26 times

2 Prescribed Motion And Dynamic Equation 190 Points A 6 Kg Collar Travels Along A Perfectly Smooth Horizontal Rod De 2 (44.06 KiB) Viewed 26 times

2 Prescribed Motion And Dynamic Equation 190 Points A 6 Kg Collar Travels Along A Perfectly Smooth Horizontal Rod De 3 (38.04 KiB) Viewed 26 times

2. Prescribed Motion and Dynamic Equation (190 points). A 6 kg collar travels along a perfectly smooth horizontal rod defined by the spiral equation r(t) = 2010, where is measured in radians, as shown in Fig. 1. The motion of the collar is produced by an external controlled electromagnetic field such that the angular velocity is prescribed and constant with a value of (1) = 4 rad/s, for all / > 0. The initial condition is 0(0) = rad.
20 18 16 Frut Frun 14 12 10 8 r(t) = €20(0) 6 6 4 e(t) 2 Ur le 6 0 -10 4 8 10 -8 02 -6 -2. -4
(a) Using the notion of time-derivative, find the angular acceleration öt), for > 0. (e) Find the velocity of the collar in polar coordinates, i.e., v(l) dr(t) di = -(t)u,(t) + upuo(t) = rur(t) +r(1)(6)uo(t). (1) Find the acceleration of the collar in polar coordinates, i.e., do(t) a(t) = =ar(t)ur(t) + aquell) di = [+6) – r(+90°c) 4,(0) + (2(ö(t) + r(t)ö() uolt). (g) Using Newton's second law, find the instantaneous total force, Flul, acting on the collar as a function of time in polar coordinates, i.e., Ftotal(t) = F(0)u,(!) + Fo(t)o(t) = m lar(1)ur() + aque(O)).