## Inertia Sentence Examples

- The numerous adjustments required by the tapper and the
**inertia**of the apparatus prompted inventors to seek for a self-restoring coherer which should not need tapping. - Mental operations are identified with physical movements, the three conditions of physical movement,
**inertia**, attraction and repulsion, being in the moral world self-love, love and hate. - But Jerome proved quite inadequate to his position, listening to the complaints of his subordinates as to want of supplies and even of pay; he spent four whole days in absolute
**inertia**, notwithstanding the emperor's reprimands. - If A is the moment of
**inertia**of the magnet, and t the time of a complete vibration, MH = 41r 2 A/t 2 (torsion being neglected). - The introduction ctf the lamina (supposed to be devoid of
**inertia**) will make no difference to the propagation of plane parallel sonorous waves through the position which it occupies. - Tons, (4) w denoting the density of water in tons/ft.', and W =wV, for a displacement of V ft.3 This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BB 1 =wAk 2 tan 8, (5) BM =BB 1 cot B=Ak e /V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak e the moment of
**inertia**of the water-line area about an axis through F, perpendicular to the plane of displacement. - Consequently the
**inertia**to overcome in moving the cylinder r=b, solid or liquid, is its own**inertia**, increased by the**inertia**of liquid (a2+b2)/(a2,..b2) times the volume of the cylinder r=b; this total**inertia**is called the effective**inertia**of the cylinder r =b, at the instant the two cylinders are concentric. - With #=o, the stream is parallel to xo, and 4)=m ch (n-a)cos = - Uc ch (n-a) sh n cos /sh (n-a) (22) over the cylinder n, and as in (12) § 29, =-Ux =-Uc ch n cos t, (23) for liquid filling the cylinder; and _ th n (14) 01 th (7 7 - a) ' over the surface of n; so that parallel to Ox, the effective
**inertia**of the cylinder n, displacing M' liquid, is increased by M'thn/th(n-a), reducing when a= oo to /If' th n = M' (b/a). - Similarly, parallel to Oy, the increase of effective
**inertia**is NT'/th n th(n-a), reducing to M'/th n=M' (a/b), when a= oo, and the liquid extends to infinity. - The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular
**inertia**of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity. - Denoting the effective
**inertia**of the liquid parallel to Ox by aW' the momentum aW'U = 4)0W' (24) _ U i -AO' 25) in this way the air drag was calculated by Green for an ellipsoida pendulum. - Similarly, the
**inertia**parallel to Oy and Oz is NW' - 1 B W', B C (b2 +-X, c 2 ab and A +C abc/ZP, Ao For a sphere a=b=c, Ao= Bo=Co =, 'a' = Q = = z, (9) U from (II), (16) so that the effective**inertia**of a sphere is increased by half the weight of liquid displaced; and in frictionless air or liquid the sphere, of weight W, will describe a parabola with vertical acceleration W - W', g (30) W+ aW Thus a spherical air bubble, in which W/W' is insensible, will begin to rise in water with acceleration 2g. - 2 V I - a /al ' Y' I-a /al ' and the effective
**inertia**of the liquid in the interspace Ao+2A1 W, =1 a13 +2a3W'. - 2A 0 - 2AI 2 a 1 3 - a3 When the spheres are not concentric, an expression for the effective
**inertia**can be found by the method of images (W. - The extension to the case where the liquid is bounded externally by a fixed ellipsoid X= X is made in a similar manner, by putting 4 = x y (x+ 11), (io) and the ratio of the effective angular
**inertia**in (9) is changed to 2 (B0-A0) (B 1A1) +.a12 - a 2 +b 2 a b1c1 a -b -b12 abc (Bo-Ao)+(B1-A1) a 2 + b 2 a1 2 + b1 2 alblcl Make c= CO for confocal elliptic cylinders; and then _, 2 A? ? - But the presence of the medium makes the effective
**inertia**depend on the direction of motion with respect to the external shape of the body, and on W' the weight of fluid medium displaced. - The effective angular
**inertia**of the body in the medium is now required; denote it by C 1 about the axis of the figure, and by C2 about a diameter of the mean section. - The moment of
**inertia**of the body about the axis, denoted by But if is the moment of**inertia**of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o. - When Montanus proposed to summon all true Christians to Pepuza, in order to live a holy life and prepare for the day of the Lord, there was nothing whatever to prevent the execution of his plan except the
**inertia**and lukewarmness of Christendom. - In that year, though the Church was under no direct threat of attack, owing to the
**inertia**of the emperor Philip the Arabian, the atmosphere was full of conflict. - If the two materials are disposed symmetrically, the amount of load carried by each would be in direct proportion to the coefficient of elasticity and inversely as the moment of
**inertia**of the cross section. - The observations are difficult, and the
**inertia**of the instrument is liable to cause error, but much care was taken. - On the other hand, under the influence of the mechanics of his day, which had hardly distinguished between
**inertia**, or the inability of a body to change itself, and resistance or the ability of bodies to oppose one another, he concluded that, as**inertia**is passive, so is resistance, and refused to recognize that in collision the mutual resistance of moving bodies is a force, or active power, of changing their movements in opposite directions. - The fact that the moment of
**inertia**of the magnet varies witli the temperature must, however, be taken into account. - When the frame of this arrangement is rapidly displaced through a small horizontal range to the right and left of the direction in which the rod points, the weight b by its
**inertia**tends to remain at rest, and the motion of the frame, which is that of the earth, is magnified in the ration op to bp. This apparatus, of which there are many types, was first introduced into seismometry by Professor Ewing. - They both protested against the political and ecclesiastical
**inertia**of their native state, and adopted the doctrines of freedom and reason. - Same is true of physical quantities such as potential, temperature, &c., throughout small regions in which their variations are continuous; and also, without restriction of dimensions, of moments of
**inertia**, &c. Hence, in addition to its geometrical applications to surfaces of the second order, the theory of quadric functions of position is of fundamental importance in physics. - The advantages of using small magnets, so that their moment of
**inertia**may be small and hence they may be able to respond to rapid changes in the earth's field, were first insisted upon by E. - Eschenhagen 2 first designed a set of magnetographs in which this idea of small moment of
**inertia**was carried to its useful limit, the magnets only weighing 1 . - It is to be remembered that all force is of the nature of a push or a pull, and that according to the accepted terminology of modern mechanics such phrases as force of
**inertia**, accelerating force, moving force, once classical, are proscribed. - The point G determined by (I) is called the mass-centre or centre of
**inertia**of the given system. - /n be the perpendicular distances from any given axis, the sum ~(mp2) is the quadratic moment with respect to the axis; it is also called the moment of
**inertia**about the axis. - Another type of quadratic moment is supplied by the deviationmoments, or products of
**inertia**of a distribution of matter. - Thus the sum ~(m.yz) is called the product of
**inertia**with respect to the planes y=o, z=o. - This may be expressed in terms of the product of
**inertia**with respect to parallel planes through G by means of the formula (14); viz.: - It appears from (24) that through any assigned point 0 three rectangular axes can be drawn such that the product of
**inertia**with respect to each pair of co-ordinate planes vanishes; these are called the principal axes of**inertia**at 0. - (28) Let us now take as co-ordinate axes the principal axes of
**inertia**at the mass-centre G. - Since the quadratic moments with respect to w and of are equal, it follows that w is a plane 01 stationary quadratic moment at P, and therefore a principal plane of
**inertia**at P. In other words, the principal axes 01**inertia**at P are the normals to the three confocals of the systen (3,~) which pass through P. Moreover if x, y, z be the co-ordinates of P, (33) is an equation to find the corresponding values of 0; and if Of, 02, 03 be the roots we find Oi+O2+81r1a2$-7, (35) - To find the relations between the moments of
**inertia**about different axes through any assigned point 0, we take 0 as origin. - Is x+y2+z(Xx+uy+vz), the moment of
**inertia**about this axis is =AX2+Bu+Cv12F~w2Gv?.2HXu, (37) provided A=~m(y+z)), B=~{m(z1+x)j, C=~m(x+y)}, ~ ~ 8 F=~(myz), G=~(mzx), H=~(mxy); 5 ~ - A, B, C are the moments of
**inertia**about the co-ordinate axes, and F, G, H are the products of**inertia**with respect to the pairs of co-ordinate planes. - The moment of
**inertia**about any radius of the quadric (39) therefore varies inversely as the square of the length of this radius. - The directions of these axes are determined by the property (24), and therefore coincide with those of the principal axes of
**inertia**at 0, as already defined in connection with the theory of plane quadratic moments. - The new A, B, C are called the principal moments of
**inertia**at 0. - The graphical methods of determining the moment of
**inertia**of a plane system of particles with respect to any line in its plane may be briefly noticed. - Provided the
**inertia**of the snrin~ itself be neglected. - Mathematical points endowed with
**inertia**coefficients, separated by finite intervals, and acting on one another with forces in the lines joining them subject to the law of equality of action and reaction. - W, or 1w, if I denote the moment of
**inertia**(~ II) about the axis. - D/dI.(Mu) =X; it shows that I measures the
**inertia**of the body as regards rotation, just as M measures its**inertia**as regards translation. - If by the attachment of another body of known moment of
**inertia**I, the period is altered from T to -r, we have T=21r,/l(I+I)(K~.