Question

Question 2. In a study of head injury against the instrument panel of a car during sudden or crash stops where lap belts without shoulder straps or airbags are used, the segmented human model shown in Fig. 2(a) is analysed. The hip joint 0 is assumed to remain fixed relative to the car, and the torso above the hip is treated as a nonuniform rigid body of mass m pivoted at 0. The centre of mass of the torso is at G, which is at a distance r from 0, with the initial position of Og taken as vertical (i.e. 0 = 0). The radius of gyration of the torso about 0 is ko. The acceleration due to gravity is denoted by g. The car is brought to a sudden stop in a crash test with a constant deceleration ac. (i). Obtain a general expression for the angular acceleration of the torso in [10 marks] terms of r, ko, 0, g, and ac after the crash (i.e. after the application of deceleration ac) considering the general position shown in Fig. 2(a) (i.e. the torso shown by dashed line).

Answer 1