# Momentum Sentence Examples

- Using her
**momentum**, he swung her over his head. - Her body continued its
**momentum**down the hill and she fell, twisting so that she wouldn't fall on the kid. - Consider a submarine boat or airship moving freely with the direction of the resultant
**momentum**horizontal, and the axis at a slight inclination 0. - Hence the angular
**momentum**of the part between A and B remains constant, or as much enters at B as leaves at A. - But the tension at P is T, parallel to the tangent, and T sin 4 parallel to PM, and through this - T sin is the
**momentum**passing out at P per second. - The velocity of propagation of a torsional disturbance along a wire of circular section may be found by the transfer of
**momentum**method, remembering that we must now replace linear**momentum**by angular**momentum**. - It was a long and wearing fight, in which the British lost 485 killed and wounded, and what was more serious, Lord Methuen (himself wounded) found that his force had exhausted its forward
**momentum**, and that he would have to collect supplies and reinforcements on the Modder before fighting his next battle. - Read on to see how that
**momentum**has built over time, and continues to build. - 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. - Equating this to the
**momentum**entering at B and subtracting P' from each X+W+p(U - u)2 =poU 2. **Momentum**(quantity of motion) is the product of mass and velocity.- In fluid movements, he shook out a noose, swung it a few times to get
**momentum**and then threw it at the limb. - The pressure on CD is equal to the A C
**momentum**which it receives per second. - Now the transfer of
**momentum**across a surface occurs in two ways, firstly by the carriage of moving matter through the surface, and secondly by the force acting between the matter on one side of the surface and the matter on the other side. - (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. - Therefore the
**momentum**entering through a square centimetre at B per second is equal to the**momentum**leaving through a square centimetre at A. - 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. - The transfer of angular
**momentum**through A is of two kinds - first, that due to the passage of rotating matter, and, secondly, that due to the couple with which matter to the right of A acts upon matter to the left of A. - 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) . - 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. - 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. - 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. - 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 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. - 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. - 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. - 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. - The total
**momentum**moving in at B is therefore P+poU 2. - In the
**momentum**equation (4) we may now omit X and it becomes 0.+P(U - u) 2 =poU2. - 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 . - On the whole the air S within ABCD neither gains nor g D loses
**momentum**, so that on the whole it receives as much through AB as it gives up to CD. - If P is the undisturbed pressure and P+w the pressure at AB, the
**momentum**entering through AB per second isJ01(P+w-+pu2)dt. - The material between A and B, though continually changing, is always in the same condition, and therefore the
**momentum**within AB is constant. - If p is the density at A, and w the cross-section, then the
**momentum**carried past A is pc,(U - u) 2. - So that no angular
**momentum**enters at B, and therefore on the whole none leaves at A. - Hence the angular
**momentum**conveyed per second outwards is 2prra 4 Ud0/dt. - Modern theory accepts the deduction, but ascribes the
**momentum**to the revolving ions in the molecules of matter traversed by the light; for the magneto-optic effect is present only in material media. - Sometimes, however, a sharp incline occurring on an otherwise easy line is not reckoned as the ruling gradient, trains heavier than could be drawn up it by a single engine being helped by an assistant or " bank " engine; sometimes also "
**momentum**" or " velocity " grades, steeper than the ruling gradient, are permitted for short distances in cases where a train can approach at full speed and thus surmount them by the aid of its**momentum**. - Now consider the
**momentum**leaving at A. - Now
**momentum**is transferred in two ways, viz. - If At seconds is the time during which the resistance of the air, R it), causes the velocity of the shot to fall Av(f/s), so that the velocity drops from v+2Av to v-2Av in passing through the mean velocity v, then (3) Rot = loss of
**momentum**in second-pounds, =w(v-+ZAv)/g - w(v - 2 Av)/g = wAv/g so that with the value of R in (I), (4) At =wAv/nd2pg. - Will have moved from 0 to 0', where 00' = Vt; and at 0' the
**momentum**is the same in magnitude as before, but its vector is displaced from OF to O'F'. - For the body alone the resultant of the components of
**momentum**W V -cos andW V sin 0 is W V -sec. lb, acting along 00', and so is unaltered. - A violent gust strikes the plate, which is driven back and carried by its own
**momentum**far past the position in which a steady wind of the same force would place it; by the time the motion has reached the pen it has been greatly exaggerated by the springiness of the connexion, and not only is the plate itself driven too far back, but also its position is wrongly recorded by the pen; the combined errors act the same way, and more than double the real maximum pressure may be indicated on the chart. - Bdo 7rpb 2 (u, b 2 a2 Uibb +¢z), and the difference X-X 1 is the component
**momentum**of the liquid in the interspace; with similar expressions for Y and Y1. - She lit with one foot underneath her body, and the
**momentum**of her fall threw her forward - over the ledge. - 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. - Since the conditions in the region PQ remain always the same, the
**momentum**perpendicular to AB entering the region at Q is equal to the**momentum**perpendicular to AB leaving the region at P. But, since the motion at Q is along AB, there is no**momentum**there perpendicular to AB.