(This question is lengthy and slightly difficult than others. Note that this is a three dimensional problem involving im

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This Question Is Lengthy And Slightly Difficult Than Others Note That This Is A Three Dimensional Problem Involving Im 1 (89.93 KiB) Viewed 51 times

(This question is lengthy and slightly difficult than others. Note that this is a three dimensional problem involving impact of two rigid bodies) A spherical ball of radius R and mass my rolls without slipping on a flat horizontal surface and has a smooth impact with a stationary bowling pin of mass m2. The velocity of the centre of mass C of the ball before impact is constant, V1 = vo vo i, in fixed frame. The bowling pin is axisymmetric with centre of mass at point C2 and principal moments I, about the vertical axis along k and I, about a horizontal axis. The position vector of point C2 with respect to Ci is, rcg Lên - be. Side view Top view VO ê i 454 B (a) (5 marks) Write expressions for unit vectors êt, en and ê, in terms of unit vectors î, j and k. (b) (5 marks) Calculate the components of angular velocities of the ball and bowling pin, denoted by w, and w, respectively, after impact, in fixed frame along unit vectors i, ſ (c) (10 marks) Calculate the components of velocities of centres of mass, C and C2, denoted by v4 and vs respectively, after impact, in fixed frame along unit vectors i, j and k. and k.