## Oy Sentence Examples

**Oy**. I have the feeling owing you is not a good thing.- "
**Oy**. That's not good," Darian said, straightening. - If three equations, each of the second degree, in three variables be given, we have merely to eliminate the six products x, 2, z 2, yz, zx, xy from the six equations u = v = w = o =
**oy**= = 0; if we apply the same process :to thesedz equations each of degree three, we obtain similarly a determinant of order 21, but thereafter the process fails. - Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-function 4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/ds = normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/ds, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream function of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity V along
**Oy**; and generally 1,1'= +Uy -Vx (4) is the relative stream-function, constant over a solid boundary moving with components U and V of velocity. - When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along
**Oy**a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp? - Taking two planes x = =b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction
**Oy**, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U - Ua 2 r2 cos 20 +mr i sin 0) (Ua 2 r 2 sin 2 0+mr 1 cos 0) + pdy (- U+Ua 2 r 2 cos 2 0 +mr1 sin 0) (Ua 2 r 2 sin 2 0 -mr 1 cos 0) =2pdymUr '(cos 0 -a 2 r 2 cos 30), (8) and with b tan r =b sec this is 2pmUdo(i -a 2 b2 cos 30 cos 0), (9) and integrating between the limits 0 = 27r, the resultant, as before, is 27rpmU. - An angular velocity R, which gives components - Ry, Ix of velocity to a body, can be resolved into two shearing velocities, -R parallel to Ox, and R parallel to
**Oy**; and then ik is resolved into 4'1+1'2, such that 4/ 1 -R-Rx 2 and 1//2+IRy2 is constant over the boundary. - Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a function ' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to
**Oy**and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current function," as it is constant along a stream line (Trans. - 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. - These equations are proved by taking a line fixed in space, whose direction cosines are 1, then dt=mR-nQ,' d'-t = nP =lQ-mP. (5) If P denotes the resultant linear impulse or momentum in this direction P =lxl+mx2+nx3, ' dP dt xl+, d y t x2' x3 +1 dtl dt 2 +n dt3, =1 ('+m (dt2-x3P+x1R) ' +n ('-x1Q-{-x2P) ' '= IX +mY+nZ, / (7) for all values of 1, Next, taking a fixed origin and axes parallel to Ox,
**Oy**, Oz through 0, and denoting by x, y, z the coordinates of 0, and by G the component angular momentum about 1"2 in the direction (1, G =1(yi-x2z+x3y) m 2-+xlz) n(y(y 3x 1 x3x y + x 2 x) (8) Differentiating with respect to t, and afterwards moving the fixed. - As the ring is moved from 0 to 0' in time t, with velocity Q, and angular velocity R, the components of liquid momentum change from aM'U +E and SM'V along Ox and
**Oy**to aM'U'+ and /3M'V' along O'x' and O'y', (I) the axis of the ring changing from Ox to O'x'; and U = Q cos 0, V = Q sin 0, U' =Q cos (o - Rt), V' =Q sin (0 - Rt), (2) so that the increase of the components of momentum, X 1, Y 1, and N1, linear and angular, are X 1 = (aM'U'+ 0 cos Rt - aM'U - - 1 3M'V' sin Rt =(a - (3)M'Q sin_(0 - Rt) sin Rt - ver Rt (3) Y 1 = (aM'U'+) sin Rt-[-13M'V' cos Rt - (3M'V = (a - (3) M'Q cos (0 - Rt) sin Rt +t sin RT, N1=[ - (aM'U'+E) sin (0 - Rt)+ 1 3M'V' cos (o - Rt)]OO' = [- (a - 1 3) M'Q cos (o - Rt) sin (o - Rt) - sin (o - Rt) ]Qt. - Mentioned above, the redactor of the Mishnah, was honoured as the "Rabbi" xar' E
**oy**v (" par excellence"), and in the tradition of the houses of learning, if it was necessary to speak of him or to cite his opinions and utterances, he was simply referred to as "Rabbi," without the mention of any name. - Adopting rectangular axes Ox,
**Oy**, in the plane of, f~ the forces, arid distinguishing FIG the various forces of the system 4. - Hence P is equivalent to three forces P1, Pm, Pu acting Ff0- 5 along Ox,
**Oy**, Oz, respectively, ~ where 1, m, n, are the direction- ratios of OH. - Or ~(Y) along
**Oy**, and a couple (x1Yiy1Xi) + (x1 YfyfXI) + - The positive directions of the axes are assumed to be so arranged that a positive rotation of 90 about Ox would bring
**Oy**into the position of UI, and so on. - From the equivalence of a small rotation to a localized vector it follows that the rotation ~ will be equivalent to rotations E,ii, ~ about Ox,
**Oy**, Uz, respectively, provided = le, s1 = me, i nc (I) and we note that li+,72+l~Z~i (2) - Whose co-ordinates are x, y, I, we draw PL normal to the plane yOz, and LH, LK perpendicular to
**Oy**, 0 - The force X1 in KH with X1 in Ox forms a couple about
**Oy**, of moment z1Xi. - Hence the force Xi can be transferred from P1 to 0, provided we introduce couples of moments z~X~ about
**Oy**and yiX1, about 01. - Dealing in the same way with the forces Yi, Zi at P1, we find that all three components of the force at P1 can be transferred to 0, provided we introduce three couples L1, Mi, Ni about Ox,
**Oy**, Oz respectively, viz. - If we take rectangular axes Ox,
**Oy**, of which**Oy**is drawn vertically upwards, we have y=sin ~ s, whence T=wy. - If P be the initial position of the particle, we may conveniently take OP as axis of x, and draw
**Oy**parallel to the direction of motion at P. If OP=a, and ~ be the velocity at P, we have, initially, x=a, y=o, x=o, y=.f0 whence x=a cos at, y=b sin nt, (10) - The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox,
**Oy**may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0. - Take, for example, the case of a sphere rolling on a plane; and let the axes Ox,
**Oy**be drawn through the centre parallel to the plane, so that the equation of the latter is 1=cf. - The moving axes Ox,
**Oy**, 01 form a rigid frame of reference whose motion at time t may be specified by the three component angular velocities p, q, r. - Now consider a system of fixed axes Ox,
**Oy**, Oz chosen so as to coincide at the instant I with the moving system Ox,**Oy**, Os.