Introductory Treatise On Rigid Dynamics

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Introductory Treatise On Rigid Dynamics
W Steadman William Steadman Aldis
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-tmzx^, +Xmyz[j^j =-Gc tm {x' + y') -^, = - 3Igy.
54. Let h be the distance of the centre of inertia from the axis of rotation, and k the radius of gyration (Art. 50) round an axis through the centre of inertia parallel to this line, the moment of inertia about the axis of z, or tm {x^ + 2/'), is therefore M¥ + l/A' (Art. 32). Also y = hsm 6.
The last equation of Art. 52 becomes M {It' + k')^ = -Mgh sine, d~6 ah . ^ /i\ a!7 = -F+F-™^ ^^)- This is the equation which determines the motion of a h^
... + k^ heavy particle suspended by a string of length — r — . This latter quantity is often called the length of the simple equivalent pendulum. The time of a small oscillation of such a pendulum of length I is shown in treatises on Dynamics of a particle to be 27r A / -, or in this case 27r 9' ^ gh ' By integrating (1) we easily obtain (Sh'^m--^' ^\ where (7 is a constant to be determined from the initial circumstances of the motion.
From (1) and (2) we can substitute the values of ^ and /dB\'^ [-T-) in the equations of the last Article, and obtain the values of F, F\ G, Q', H+IF, MOTION ROUND A FIXED AXIS.


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