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  
a  a  a  (1.28)
n
or in a scalar form the modulus of the total acceleration is equal to

2 2
a  a n  a  . (1.29)
The modulus of instantaneous tangential acceleration can be presented
as the next derivative

dv
a  2 . (1.30)
n
dt
where dv is the base of triangle with infinitely small vertex angle
2
d  , therefore

dv  v d   (1.31)
2

For the infinitely small interval of time dt the material point
passes infinitely small distance dS as elementary arc of circle of

radius r, consequently
dS  r d   (1.32)

Taking into account ( 1.24)
v dS
a   , (1.33)
n
r dt

dS
where  v , we obtain the modulus of normal acceleration
dt
2
v
a  (1.34)
n
r .

This acceleration is often called the centripetal acceleration

because it is directed to the centre of curvature of a curve. Оobviously,
when the material point moves by circle , r is the radius of this circle.

1.6. Absolutely (Perfectly) Rigid Body .The Number of Rigid Body

Degrees of Freedom. Types of Motion.

In physics, a rigid body is an idealization of a solid body of finite

size in which deformation is neglected. In other words, the distance
between any two given points of a rigid body remains constant in time

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