Month: December 2025

📘 Oscillations & Special Theory of Relativity

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UG Physics (Honours) Notes 🔹 1️⃣ Oscillations ⭐ Simple Harmonic Motion (SHM) A body performs SHM when acceleration is directly proportional to displacement and directed towards the mean position:a=−ω2xa = -\omega^2 xa=−ω2x General solution:x(t)=Acos⁡(ωt+ϕ)x(t) = A\cos (\omega t + \phi)x(t)=Acos(ωt+ϕ) ⭐ Resonance Maximum amplitude occurs at:ω=ω0=km\omega = \omega_0 = \sqrt{\frac{k}{m}}ω=ω0​=mk​​ Quality Factor: Q=ω02γQ = \frac{\omega_0}{2\gamma}Q=2γω0​​ … Read more

🌍 Gravitation & Central Force Motion

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UG Physics (Honours) Notes ⭐ Newton’s Law of Gravitation Newton stated that every two masses in the universe attract each other with a force:F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}F=Gr2m1​m2​​ ✳ Differential Equation of Motion μr⃗¨=F⃗(r)\mu \ddot{\vec{r}} = \vec{F}(r)μr¨=F(r) 🌟 First Integrals of Motion 1️⃣ Angular Momentum ConservationL⃗=μr2θ˙=constant\vec{L} = \mu r^2 \dot{\theta} = \text{constant}L=μr2θ˙=constant 2️⃣ Energy ConservationE=12μr˙2+L22μr2+U(r)=constantE = … Read more

📘 Elasticity & Fluid Motion

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UG Physics (Honours) Notes 1️⃣ Elasticity Elasticity is the property of a material by which it returns to its original shape after removing external forces. Flexural Rigidity Flexural Rigidity=YI\text{Flexural Rigidity} = YIFlexural Rigidity=YI Higher value → more resistance to bending. Cantilever Beams Type Deflection Formula Example Use Single Cantilever δ=WL33YI\delta = \frac{W L^3}{3 Y I}δ=3YIWL3​ Diving board … Read more

Rotational Dynamics & Non-Inertial Systems

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UG Physics (Honours) Notes 1️⃣ Rotational Dynamics Rotational motion deals with bodies that rotate about an axis. Just like linear motion involves force and momentum, rotation involves torque and angular momentum. Rotation About a Fixed Axis Moment of Inertia (MI) MI is the rotational equivalent of mass:I=∑miri2I = \sum m_i r_i^2I=∑mi​ri2​ Dependence: Theorems Used for … Read more

ଧର୍ମାନ୍ତର ଓ ହିନ୍ଦୁ ସଂସ୍କୃତି ସୁରକ୍ଷା – ଇତିହାସ, ବର୍ତ୍ତମାନ ଓ ସମାଧାନ

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ଧର୍ମାନ୍ତରର ଇତିହାସ ଓ ହିନ୍ଦୁ ସଂସ୍କୃତି ସୁରକ୍ଷା: ଏକ ସଚେତନତାମୂଳକ ଅଧ୍ୟୟନ (Case Studies ସହିତ)   —   ଇତିହାସର ନଜରିଆ   ଭାରତରେ ବିଦେଶୀ ଆକ୍ରମଣ ସହିତ ଅନେକ ଧର୍ମୀୟ ପ୍ରଭାବ ଆସିଥିଲା। ମଧ୍ୟଯୁଗରେ କେତେକ ଅଞ୍ଚଳରେ—   ଜବରଦସ୍ତି ଧର୍ମାନ୍ତର   କଥିତ ଅବମାନନାକାରୀ ପ୍ରଚାର   ଧର୍ମୀୟ ସଂସ୍କୃତିକ ପ୍ରତୀକର ଉଚ୍ଛେଦ     ଘଟିଥିବା ଲେଖାଜୋଖା ଇତିହାସ ପୁସ୍ତକ ଓ ତଥ୍ୟରେ ମିଳେ।   ସେହିପରି, ଉପନେବଶୀ ଯୁଗରେ ମିଶନରୀମାନେ … Read more

Vector Differentiation and Vector Integration

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Calculus – II | Undergraduate Mathematics Notes Vectors play a crucial role in describing physical quantities such as force, velocity, electric and magnetic fields. Vector calculus deals with the differentiation and integration of vector fields in space. 🔹 1️⃣ Vector Differentiation Directional Derivative Measures the rate of change of a scalar field in a given … Read more

Orthogonal Curvilinear Coordinates and Dirac Delta Function

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Calculus – II | Undergraduate Mathematics In many physical and engineering problems, the geometry of motion or fields may not be suitable for Cartesian (x, y, z) coordinates. To handle such problems efficiently, Orthogonal Curvilinear Coordinate Systems like Cylindrical and Spherical are used. This chapter also introduces an important mathematical tool — the Dirac delta … Read more

Calculus – II: Functions of Several Variables and Vector Algebra

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For Undergraduate Students Calculus–II extends the concepts of single-variable calculus into functions of more than one variable. It is an essential mathematical tool for Physics, Chemistry, Engineering, Computer Science, and Economics. This chapter introduces partial derivatives, optimization, and vector algebra, which are widely used in real-world problem solving. 🔹 1️⃣ Calculus of Functions of More … Read more

Calculus – I

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Calculus is one of the most important areas of Mathematics for undergraduate students across science, commerce, and engineering streams. It helps us understand how quantities change and provides tools for modeling real-world problems in physics, economics, biology, and engineering. This article covers the core topics of Calculus – I, including plotting of functions, continuity, differentiability, … Read more