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By G. H. Ryder, M. D. Bennett (auth.)

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1 may then be applied independently in the x- and y-directions, with time as the linking parameter. 11 A gun is to be laid so that the shell will strike a target 3000 m away in the horizontal direction and 240m higher in elevation. If the muzzle velocity is 850 m/s, determine the time t taken for the shell to reach the target, the barrel elevation (),and the velocity of the shell v, when it strikes. 81 m/s 2 downwards due to gravity. I a are then applicable. 55 s The first solution corresponds to a very high trajectory with the barrel almost vertical, and is rather impractical.

2 (kc gl+ p)-t l:[gl 2 X 21-(kc 2 + P)g] (g/) 2 hence therefore If the pivot point 0 is at G, then there can be no moment about 0 and the time for one oscillation will be infinite. Since there is only one solution, it follows that it must define a minimum time. 3 lists the expressions for the moment of inertia of some common bodies. 3 MOMENTS OF INERTIA Moment of Inertia Body Uniform rod A F===:::i~========! I. 3 General Plane Motion of a Rigid Body In this case it is generally more convenient to consider a moment sum about the mass centre.

Since friction opposes the tendency to move, the particle will ultimately slide outwards. 2 rad/s. 36a, subjected to a number of external forces of which only three, F 1 , F 2 and F 3 are shown. A typical particle of mass m; is located at the point (x;,y;), and the point G having co-ordinates XG and YG is the mass centre of the system. 36b is a free· body diagram for the particle. 36 act directly on m;, and there will also be internal forces or reactions from adjacent particles. 30 F; 1 + F; 2 + F; 3 +(reactions from adjacent particles)= mia;.

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