ورقة مفاهيم Dynamics للصف الثالث الثانوي 2026.. حمل كراسة الوزارة pdf

أعلنت وزارة التربية والتعليم والتعليم الفني رسميا إتاحة ورقة مفاهيم Dynamics للصف الثالث الثانوي 2026 عبر موقعها الإلكتروني المعتمد لمساعدة طلاب مدارس اللغات في مراجعة القواعد والاشتقاقات الرياضية المعقدة المقررة في منهج الرياضيات التطبيقية وتوفير الدعم التعليمي اللازم لهم قبيل انطلاق ماراثون امتحانات نهاية العام الدراسي.

ورقة مفاهيل ديناميكا لغات تالتة ثانوي 2026

تهدف وزارة التربية والتعليم من خلال نشر هذه الكراسات والمجلدات الرسمية إلى توفير مرجع قانوني موحد للطلاب يعفيهم من حفظ المعادلات والاشتقاقات الرياضية الطويلة داخل لجان الامتحانات، حيث يتضمن المحتوى المفرغ بدقة من الأوراق الرسمية المعتمدة في كراسة المفاهيم مرتبة بالكامل:

Applied Mathematics (Dynamics)
Differentiation and Integration of vector functions:
If each of s, v, x are functions in the time then v
If a is a function in the position, then a = v \frac{dv}{dx} \Rightarrow \int a dx = \int v dv
If a is a function in the displacement, then a = v \frac{dv}{ds} \Rightarrow \int a ds = \int v dv

The average velocity: v_a = \frac{\text{Total distance}}{\text{Total time}}
The average velocity vector: \vec{v_a} = \frac{\text{Total displacement}}{\text{Total time}}
The motion is accelerated if (va > 0)
The motion is (decelerated) if (va < 0)
The momentum of a body at a moment is a vector quantity whose magnitude is equal to the product of the mass of this body by its velocity at this moment and its

direction is the direction of the velocity itself.
\therefore \vec{H} = m \vec{v}
The change of the momentum of a body = m(\vec{v_2} - \vec{v_1})
\Delta H = m \int_{t_1}^{t_2} a dt
If the acceleration a is a function of time t.
Newton's First Law
Every body preserves in its state of rest or of moving uniformly unless acted upon by an unbalanced external force by an external effect.
Newton's second law

A body whose mass is m and moves with a uniform acceleration a:
ma = F where F is the resultant of the forces acting on the body.
If a = \frac{dv}{dt}, then the equation of motion is in the form: \int_{t_1}^{t_2} F dt = m \int_{v_1}^{v_2} dv
If a = v \frac{dv}{ds}, then the equation of motion is in the form: \int_{s_1}^{s_2} F ds = m \int_{v_1}^{v_2} v dv
If the mass is variable, then the equation of motion is in the form: F = \frac{d}{dt}(m v)

The units used with the equation of motion
m(\text{kg}) \cdot a(\text{m/sec}^2) = F (\text{newton})
m(\text{gm}) \cdot a(\text{cm/sec}^2) = F (\text{dyne})
Applications on Newton's laws of moving a body inside a lift
The lift at rest or moving with a uniform velocity: mg = N
The lift ascends with acceleration (a): N - mg = ma
The lift descends with acceleration (a): mg - N = ma

Where N (appearing weight), (reading of the balance) or (reaction of the lift's ground)
Applications on Newton's laws of a body suspended in a spring balance
The lift at rest or moving with a uniform velocity: mg = T
The lift ascends with acceleration (a): T - mg = ma
The lift descends with acceleration (a): mg - T = ma
Where T (is the tension in the spring balance)