If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If a system consists of several particles, the total angular momentum about a point can be obtained by adding ( or integrating ) all the angular momenta of the constituent particles.

If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.

If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.

If an opponent tries to anticipate the stroke, he may move in the wrong direction and may be unable to change his body momentum in time to reach the shuttlecock.

If the truck were lighter, or moving slower, then it would have less momentum.

If two particles have masses and, and velocities and, the total momentum is

If the center of mass is moving at velocity, the momentum is:

If a force is applied to a particle for a time interval, the momentum of the particle changes by an amount

If the force depends on time, the change in momentum ( or impulse ) between times and is

If the velocities are and before the collision and and after, the equations expressing conservation of momentum and kinetic energy are:

If one body is motionless to begin with, the equation for conservation of momentum is

If a coordinate is not a Cartesian coordinate, the associated generalized momentum component does not necessarily have the dimensions of linear momentum.

If momentum is to be conserved in a volume, changes in the momentum of matter through the Lorentz force must be balanced by changes in the momentum of the electromagnetic field and outflow of momentum.

If is the momentum of all the particles in a volume, and the particles are treated as a continuum, then Newton's second law gives

If a charged particle moves in an electromagnetic field, its kinematic momentum is not conserved.

If the particle is in an eigenstate of position, then its momentum is completely unknown.

If so many voters give their first preferences to the " weak " candidate that it ends up winning the first round, it is highly likely they will gain enough campaign momentum to have a strong chance of winning the runoff, too, and with it, the election.

If multiple torques are acting on the body, it is instead the net torque which determines the rate of change of the angular momentum:

If the position was found to be r < sub > 0 </ sub > then in an interpretation satisfying CFD, the statistical population describing position and momentum would contain all pairs ( r < sub > 0 </ sub >, p ) for every possible momentum value p, whereas an interpretation that rejects counterfactual values completely would only have the pair ( r < sub > 0 </ sub >,⊥) where ⊥ denotes an undefined value.

If the average momentum gained from inward traffic equals that imparted to outward traffic, there is no net energy cost, and thus nothing to recoup.

Jarry once wrote, expressing some of the bizarre logic of ' pataphysics, " If you let a coin fall and it falls, the next time it is just by an infinite coincidence that it will fall again the same way ; hundreds of other coins on other hands will follow this pattern in an infinitely unimaginable fashion ".

If the coin is judged favorably in all of these criteria, it will generally be awarded a higher grade.

If the teams remain tied, overtime periods continue, with a coin flip determining the first possession.

If a coin is greatly lacking in all of these, it is unlikely to be worth much.

If the coin is fair, then the probability of the next flip being heads is 1 / 2.

If one flips a coin 21 times in a row and obtains 21 heads, one might rationally conclude a high probability of bias towards heads, and hence conclude that future flips of this coin are also highly likely to be heads.

If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted.

One may ask " If I were to flip a fair coin 100 times, what is the probability of it landing heads-up every time?

If we are tossing a coin, then the negative binomial distribution can give the number of heads (“ success ”) we are likely to encounter before we encounter a certain number of tails (“ failure ”).

If V is a probabilisitic Turing Machine which could possible accept x if x is in X, then the proof is the string of coin flips which leads the machine, by luck, intuition, or genius, to accepting x.

If we know not just, but the earlier values as well, then we can determine which coins have been drawn, and we know that the next coin will not be a nickel, so we can determine that with probability 1.

“ If the head-side is up, the game would be called Mei-Chu ; otherwise, the game would be called Chu-Mei .” As the head-side of the coin went up, the tournament was thereby named Meichu to commemorate the two founding presidents of NTHU and NCTU, Dr. Mei Yi-Chi, and Dr. Ling Chu-Ming.

Let the coin tosses be represented by a sequence of independent random variables, each of which is equal to H with probability p, and T with probability Let N be time of appearance of the first H ; in other words,, and If the coin never shows H, we write N is itself a random variable because it depends on the random outcomes of the coin tosses.

If the black box works then the coin does not drop.

" If someone comes to my grave, gives a coin to charity, and says these ten Psalms Tikkun HaKlali, I will pull him out from the depths of Gehinnom!

If the employer had deduced from the interviews so far that both candidates would complete the task in somewhere between 195 and 205 hours, it would be in the employer's best interests to choose one or the other by some easily-applied metric ( for example, flipping a coin ) rather than spend the $ 100 on determining the better candidate, saving at most $ 100 in labor.

If part of the die chips out, showing as a raised, unstruck area on the coin, it is called a chip.

If he found people drinking from a fountain, he gave them a half-crown coin.

If not provided for on the obverse, the reverse side usually contains information relating to a coin's role as medium of exchange ( such as the value of the coin ).

# If Alice's revelation matches the coin result Bob reported, Alice wins

:( 1 ) If the coin had been flipped, it would have landed heads.