Lesson 2.10 • Competency 2.6Complete Lesson
Back to UnitRotational Dynamics & Moment of Inertia
Torque (τ), moment of inertia (I), rotational Newton’s law (τ = Iα), angular momentum conservation (L = Iω), and rolling kinetic energy.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- State and apply the rotational analogue of Newton’s second law: τ = I α.
- Apply conservation of angular momentum to isolated rotating systems (e.g. spinning figure skater, collapsing star).
Core Theory & Concepts
Rotational dynamics parallels translational mechanics: torque replaces force, moment of inertia replaces mass, angular velocity replaces linear velocity, and angular momentum replaces linear momentum.
Rotational Newton’s Law
Applied torque causes angular acceleration: τ = I · α, where I is moment of inertia.
τ = I · α
Conservation of Angular Momentum
When net external torque is zero (Στ_ext = 0), total angular momentum remains constant: I₁ ω₁ = I₂ ω₂.
L = I · ω = ext{constant}
Common Misconceptions
Misconception
Believing moment of inertia depends only on total mass.
Physical Clarification:Moment of inertia depends heavily on HOW mass is distributed relative to the axis of rotation (I ∝ m r²). A hollow cylinder has twice the moment of inertia of a solid cylinder of the same mass and radius.
Syllabus Topic Outline
- 1Concept of torque τ = r × F and angular acceleration α
- 2Moment of inertia I = Σ m_i r_i² of continuous and discrete bodies
- 3Rotational kinetic energy E_rot = ½ I ω²
- 4Conservation of angular momentum L = I ω