[no1]

Kinetic energy
(also called vis viva, or living force)
this energy possessed by a body by virtue of its motion
The kinetic energy of a body is equal to the amount of work
needed to establish
its velocity and rotation
starting from rest
Equations
Definition



the words in the above
equation state that the kinetic energy (Ek) is
equal to the integral of the dot product
of the velocity (v) of a body
and the infinitesimal of the body's momentum (p)

[no1]

Newtonian mechanics
For non-relativistic mechanics
the total kinetic energy of a body can be considered
as the sum of the body's translational
kinetic energy and its rotational energy
or angular kinetic energy



where
Ek is the total kinetic energy
Et is the translational kinetic energy
Er is the rotational energy or angular kinetic energy

[no1]

For the translational kinetic energy of a body
with mass m
whose centre of mass is moving in a straight line
with linear velocity v
we can use the Newtonian approximation



where:
m is mass of the body
v is linear velocity of the centre of mass body
Thus, for a speed of 10 m/s the kinetic energy is 50 J/kg, for a speed of 100 m/s it is 5 kJ/kg, etc.

[no1]

If a body is rotating
its rotational kinetic energy or angular kinetic energy is calculated from

where
I is the body's moment of inertia
ω is the body's angular velocity.

[no1]

Relativistic mechanics
In Einstein's relativistic mechanics
(used especially for near-light velocities)
the kinetic energy of a body is






where:
Ek is the kinetic energy of the body
v is the velocity of the body
m is its rest mass
c is the speed of light in a vacuum.
γmc2 is the total energy of the body
mc2 is the rest mass energy (90 petajoule/kg)

[no1]

It is an edifying exercise to show
that the ratio of this relativistic kinetic energy
to the Newtonian kinetic energy given
by





This can be done by the techniques of first-year calculus.
Relativity theory states
that the kinetic energy of an object
grows towards infinity
as its velocity approaches the speed of light
and thus that it is impossible to accelerate an object to this boundary

[no1]

Where gravity is weak
and objects move at much slower velocities than light
(e.g. in everyday phenomena on Earth)
Newton's formula is an excellent approximation of relativistic kinetic energy
The next term in the approximation is



for a speed of 10 km/s this is 0.04 J/kg
for a speed of 100 km/s it is 40 J/kg, etc.
The exact Taylor series is



Heat as kinetic energy

للطاقة الحركيّة ديمومة ساخنه
الحرارة شكل من أشكال الطاقةِ
و تكون بسبب الطاقةِ الحركيّةِ الكليّةِ للجزيئاتِ وذرّاتِ الكتلة
إنّ العلاقةَ بين الحرارةِ
درجة الحرارة و الطاقة الحركيّة
هي مِنْ الذرّاتِ والجزيئاتِ
موضوعُ الميكانيكا الإحصائيةِ

في أنّ آي تغيّرُ بالطاقةِ الداخليةِ
ينحو منحني الطاقة لتمثيله حراريا

تلك الطاقة الحراريةِ الممثّلُة
تُشيرَ إلى أن الطاقةِ
و بشكل مُحدّد
إرتبطتْ بالحركةِ العشوائيةِ translational للذرّاتِ والجزيئاتِ
و في بَعْض الكتل المميّزةِ تكون ضمن النظام
فتُشكّلُ حمايةُ حراريةِ
من خلال العملِ الميكانيكيِ
القانونِ الأولِ للديناميكا الحراريةِ

[خلف الجميلي]

بارك الله فيك

ولكن ليتها ترجمت

[جـــــــود]

جزيت خيــــــــــراً .............

[no1]

شكرا مروركما الكريم
إن شاء الله أستاذ جميلي
و لكن هل تري أنها محتاجه لترجمه
ظننتها واضحه