Read and translate the text. Think out a headline

We know the velocity of a particle to be continuously changing if this particle has nonuniform motion; in each successive time inter­val the particle acquires or takes on some increment of velocity. The time rate at which the velocity changes is the acceleration of particle. This rate has magnitude, according to how much velocity is being taken on per unit of time, and direction, according to the direction of the velocity that is being taken on. The magnitude of acceleration is expressed in units of velocity per unit of time, as miles per hour per minute (mi/hr/min) or feet per second per second (ft/sec/sec or ft/sec).

The direction of the acceleration is conveniently indicated by sign, plus when to the right, minus when to the left.

If the velocity changes uniformly (equal velocity increments in all equal intervals of time), then the acceleration is constant and may be computed by dividing the velocity-increment for any interval of time by the interval. That is a = Δ v:Δ t (1) where Δ v denotes the velocity incre­ment for the interval Δ t.

If the velocity does not change uniformly, then the acceleration is not constant but changes continuously, and Eq. 1 does not, in gener­al, give the acceleration at any particular instant but gives only aver­age acceleration for the interval Δ t.

That is, αα = Δ v:Δ t (2) where αα denotes average acceleration. The acceleration at a particular instant is the limit of the average accele­ration for an interval that includes the instant in question (in question - рассматриваемый; in question - зд. является определением) as the interval is taken smaller and smaller.

This limit is dv/dt; that is α = dv:dt (3). If we substitute for v its value ds/dt, Eq, 3 becomes α = ds/ dt.

The above equations indicate that αα and α are positive or nega­tive according to the sign of Δ v or dv, and this is consistent with the rule for the sign of acceleration given above. It should be particu­larly noted that the sign of the acceleration does not depend merely on whether the speed is increasing or decreasing.

If a particle is moving to the right and going faster and faster it has positive acceleration, but it also has positive acceleration when moving to the left and going slower and slower. In both cases positive velocity is being taken on and the direction of the accelera­tion is to the right. The magnitude of the acceleration, without regard to sign, represents the rate of change of speed [2, С. 53 - 54].

2.5.5 Look through the text and find the English equivalents for the following Russian phrases and word-combinations:

в каждый последующий интервал времени; за единицу времени; изменяется равномерно; постоянно изменяется; означает среднее ускорение; уравнения выше; в обоих случаях.

2.5.6 Read and translate the text, give brief definitions to angular velocity, angular acceleration, rotary inertia and explain Newton’s second law for rotary motions.