## Momentum Sentence Examples

- Hence the angular
**momentum**of the part between A and B remains constant, or as much enters at B as leaves at A. - If the velocity of a particle at A relative to the undisturbed parts is u from left to right, the velocity of the matter moving out at A is U - u, and the
**momentum**carried out by the moving matter is p(U - u) 2. - There is also the " external " applied pressure X, and the total
**momentum**flowing out per second is X-I-P4-W-1-p(U - u)2. - In fluid movements, he shook out a noose, swung it a few times to get
**momentum**and then threw it at the limb. - (2) y The rate of generation of
**momentum**in the interior of S by the component of force, X per unit mass, is fffpXdxdydz, f pXdxdydz, (3) and by the pressure at the surface S is -f. - Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total
**momentum**F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) . - At B there is only the latter kind, and since the transfer of matter is powoU, where po is the undisturbed density and wo is the undisturbed cross-section, since its velocity is U the passage of
**momentum**per second is powoUo 2. - Sulpicius Galba and others, and along with it the development of prose composition, went on with increased
**momentum**till the age of Cicero. - In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the
**momentum**and the energy at an element of volume of the molecular medium, with the precision necessary in order that the dynamical equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid - a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved. - But the matter to the right of A is also receiving
**momentum**from the matter to the left of it at the rate indicated by the force across A. - Long previously Lord Kelvin himself came nearer this view, in offering the opinion that magnetism consisted, in some way, in the angular
**momentum**of the material molecules, of which the energy of irregular translations constitutes. - The time rate of increase of
**momentum**of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations. - 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. - Well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the
**momentum**of the medium, the**momentum**of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance. - 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. - Since the condition of the medium between A and B remains constant, even though the matter is continually changing, the
**momentum**possessed by the matter between A and B is constant. - The equations of motion can be established in a similar way by considering the rate of increase of
**momentum**in a fixed direction of the fluid inside the surface, and equating it to the**momentum**generated by the force acting throughout the space 5, and by the pressure acting over the surface S. - Taking the fixed direction parallel to the axis of x, the time-rate of increase of
**momentum**, due to the fluid which crosses the surface, is - f'fpuq cos OdS = - f f (lpu 2 -+mpuv+npuw)dS, (1) which by Green's transformation is (d(uiu 2) dy dz dxdydz. - The partial differential coefficient of T with respect to a component of velocity, linear or angular, will be the component of
**momentum**, linear or angular, which corresponds. - Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of
**momentum**, the partial differential coefficient with respect to a**momentum**component will give the component of velocity to correspond. - Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of
**momentum**corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =.. - 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. - In the absence of a medium the inertia of the body to transtion is the same in all directions, and is measured by the (3) But the change of the resultant
**momentum**F of the medium as. - On the other hand, if the effects arose from balanced stresses set up inside the globe by the radiation, the effects on the vanes and on the case would be of the nature of action and reaction, so that the establishment of motion of the vanes in one direction would involve impulsion of the case in the opposite direction; but when the motion became steady there would no longer be any torque either on the vanes or on the case, and the latter would therefore come back to its previous position of equilibrium; finally, when the light was turned off, the decay of the motion of the vanes would involve impulsion of the case in the direction of their motion until the moment of the restoring torque arising from the suspension of the case had absorbed the angular
**momentum**in the system. - When A is held still, and B rotated, centrifugal action sets up vortex currents in the water in the pockets; thus a continuous circulation is caused between B and A, and the consequent changes of
**momentum**give rise to oblique reactions. - But it has velocity U, and therefore
**momentum**poU 2 is carried in. - In addition there is a pressure between the layers of the medium, and if this pressure in the undisturbed parts of the medium is P,
**momentum**P per second is being transferred from right to left across each square centimetre. - Substituting in the
**momentum**equation, we obtain Pv 1 7V + y 2 I V / +PoU 2 I - v) V) = PoU2, whence U 2 = Po (I }-y21 U J . - Since no angular
**momentum**goes out on the whole Z nwra 4 d0/dx -?- 2 pwra 4 Ud0/dt = o. - Lord Kelvin was thereby induced to identify magnetic force with rotation, involving, therefore, angular
**momentum**in the aether. - The total
**momentum**moving in at B is therefore P+poU 2.