A car trying to break into a secure industrial area collides with a spring- loaded "swing away" security gate. The gate can be modeled as a bar with a torsional spring mounted at the pivot point, as shown in the schematic. The mass moment of inertia of the bar about the axis through point O is lo= 900 kg-m, and the torsional stiffness of the spring is = 4500 N-m. The car has a mass m = 1965 kg and hits the gate at point P, as shown in the schematic. If velocity of the car just prior to collision is v = 30 m/s and the coefficient of restitution of the collision, e = 0.71, determine: (a) the angular velocity of the gate immediately after the collision, and (b) the maximum angular displacement of the gate, 0 (in radians). e 2.4 m