घूर्णन गतिशास्त्र
Equations of angular motion, moment of inertia, radius of gyration, torque and angular acceleration, rotational kinetic energy, angular momentum and its conservation, work and power in rotational motion.
Comprehensive notes covering angular kinematic variables, moment of inertia of rigid bodies, torque and angular acceleration, rotational kinetic energy, and the law of conservation of angular momentum.
Note: This expression is strictly analogous to linear translational kinetic energy K_trans = (1/2) * m * v², where moment of inertia I replaces mass m and angular velocity ω replaces linear velocity v.
Note: For a disc, 2/3 (66.67%) of the kinetic energy is translational and 1/3 (33.33%) is rotational.
High-probability exam questions curated specifically for Rotational Dynamics.
Exam Rationale: Directly maps to CDC Specification Grid LO 1.3: Acceleration of rolling bodies on an inclined plane. Frequently tested as a 4-mark theoretical derivation or numerical.
Exam Rationale: Directly addresses CDC Specification Grid LO 1.2: Relation between torque and angular momentum, conditions of equilibrium, and conservation principles. Core 4-mark theoretical board question.
Exam Rationale: Assesses deep conceptual understanding of the role of static friction in rolling without slipping, derivation of limiting friction coefficient, and mechanical energy conservation.
Exam Rationale: Theorem of Parallel Axes and Theorem of Perpendicular Axes are core syllabus items in CDC Unit 1. Frequently asked to determine moment of inertia for standard symmetric shapes.
⚠️ Common Error: Using revolutions per minute (rpm) directly in kinematic or kinetic energy formulas.
✓ Correct Approach: Always convert rpm to rad/s using $\omega = \frac{2\pi N}{60}$ before calculations.
Why: Equations of motion and kinetic energy derived in SI units require angular velocity in radians per second.
⚠️ Common Error: Applying the perpendicular axis theorem ($I_z = I_x + I_y$) to solid spheres or cylinders.
✓ Correct Approach: Use the perpendicular axis theorem strictly for thin planar lamina bodies (e.g. flat circular discs, rectangular sheets).
Why: In 3D solid objects, the $z$-coordinate of constituent mass particles is non-zero, violating the mathematical assumption $z_i = 0$.
⚠️ Common Error: Forgetting rotational kinetic energy when an object rolls down an incline without slipping.
✓ Correct Approach: Use $mgh = \frac{1}{2} m v^2 + \frac{1}{2} I \omega^2$, NOT simply $mgh = \frac{1}{2} mv^2$.
Why: Gravitational potential energy converts into both linear translational motion of the center of mass and spin rotation about the center of mass.
Ministry of Education, Science and Technology, Government of Nepal
Aligned with NEB Class 12 Physics syllabus code Phy.102 Unit 1 (Rotational Dynamics).
National Examinations Board, Sanothimi, Bhaktapur
Unit weightage: 6 marks (1 MCQ + 1 Short Answer or Numerical).