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NEB Class 12 Physics Rotational Dynamic Note Handwritten in PDF
What is Rotational Dynamics?
Rotational dynamics is the branch of physics that studies the motion of objects rotating about a fixed axis. In NEB Class 12 Physics (2082 curriculum), this is the very first chapter and carries heavy exam weightage — expect 7 to 11 marks in your board paper. The chapter is essentially the rotational version of everything you studied in linear dynamics in Class 11, so if you understand that foundation, rotational dynamics becomes much easier.
Equations of Angular Motion
Angular motion has its own set of kinematic equations, directly parallel to the linear equations you already know.
- Angular displacement (θ) — the angle rotated, measured in radians
- Angular velocity (ω) — rate of change of angular displacement (rad/s)
- Angular acceleration (α) — rate of change of angular velocity (rad/s²)
The three equations of angular motion are:
- ω = ω₀ + αt
- θ = ω₀t + ½αt²
- ω² = ω₀² + 2αθ
These are identical in structure to v = u + at, s = ut + ½at², and v² = u² + 2as. In the NEB exam, a common question asks you to compare linear and angular motion equations in a table — make sure you can do this.
Kinetic Energy of Rotation
When a rigid body rotates, every particle in it has kinetic energy due to its speed. The total rotational kinetic energy is:
KE(rotational) = ½Iω²
This is the rotational equivalent of KE = ½mv². Here, I (moment of inertia) plays the role of mass, and ω (angular velocity) plays the role of linear velocity.
Moment of Inertia and Radius of Gyration
Moment of inertia (I) is the most important concept in this chapter. It is the rotational equivalent of mass — it measures how difficult it is to start or stop a rotation.
- Formula: I = Σmᵢrᵢ² (sum of mass × distance² for every particle)
- Unlike mass, moment of inertia depends on where the mass is located relative to the axis
- Mass concentrated far from the axis gives a larger I (harder to rotate)
- Mass concentrated near the axis gives a smaller I (easier to rotate)
Radius of gyration (K): The distance from the axis at which the entire mass could be placed to give the same moment of inertia. Formula: I = MK², so K = √(I/M)
Important derivations for NEB exam:
- MI of thin uniform rod about its centre = ML²/12
- MI of thin uniform rod about its one end = ML²/3
- Both derivations use integration and are 4-mark questions in the board exam
Torque and Angular Acceleration
Torque (τ) is the rotational equivalent of force. It is what causes angular acceleration.
- Formula: τ = r × F = rF sinθ
- The fundamental equation: τ = Iα (rotational form of F = ma)
- Larger torque → greater angular acceleration
- Larger moment of inertia → smaller angular acceleration for same torque
Work done in rotation: W = τθ
Power in rotation: P = τω
Angular Momentum and Its Conservation
Angular momentum (L) is the rotational equivalent of linear momentum.
- Formula: L = Iω
- Rate of change: τ = dL/dt (torque = rate of change of angular momentum)
Principle of Conservation of Angular Momentum: If no external torque acts on a system, its total angular momentum remains constant.
L = Iω = constant (when τ_external = 0)
Real-life examples:
- A spinning ice skater pulls arms inward → I decreases → ω increases → stays in the air longer
- A diver tucks their body → I decreases → spins faster
- Earth’s rotation is conserved because no external torque acts on it
This conservation principle is frequently asked as a 2-mark short question or as a 4-mark numerical in NEB exams.
Key Formulas at a Glance
| Quantity | Linear | Rotational |
|---|---|---|
| Inertia | m | I = Σmr² |
| Newton’s 2nd Law | F = ma | τ = Iα |
| Kinetic Energy | ½mv² | ½Iω² |
| Momentum | p = mv | L = Iω |
| Work | W = Fs | W = τθ |
| Power | P = Fv | P = τω |
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FAQs
What is the moment of inertia in Class 12 Physics NEB?
Moment of inertia (I) is the rotational equivalent of mass. It measures an object’s resistance to angular acceleration. For a uniform rod of mass M and length L rotating about its center, I = ML²/12. It depends on both mass and the distribution of mass relative to the axis of rotation.
What is the difference between torque and angular momentum?
Torque (τ) is the rotational equivalent of force — it causes angular acceleration (τ = Iα). Angular momentum (L = Iω) is the rotational equivalent of linear momentum. Torque is the rate of change of angular momentum: τ = dL/dt.
Is angular momentum conserved in rotational dynamics?
Yes. The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum remains constant. A classic example is a spinning ice skater who pulls in arms to spin faster (I decreases, ω increases, L stays constant).
What formulas are most important in Rotational Dynamics for NEB exam?
The key formulas are: (1) τ = Iα, (2) L = Iω, (3) KE(rotational) = ½Iω², (4) Conservation: I₁ω₁ = I₂ω₂, (5) MI of rod about center = ML²/12, about one end = ML²/3. Numerical problems frequently use these in NEB board exams.
How many marks does Rotational Dynamics carry in NEB Class 12 Physics?
Rotational Dynamics typically carries 7–11 marks in the NEB Physics board exam. It includes short answer questions (2 marks each) and numerical problems (4 marks each). Understanding derivations of MI and torque-angular acceleration relation is essential for full marks.