Introduction
This unit extends Newtonian mechanics to rotational motion, focusing on how objects rotate and what causes changes in their rotational state. It mirrors linear dynamics but uses angular quantities like torque, angular acceleration, and moment of inertia.
Torque: A twisting force, calculated as τ = r·F·sin(θ).
Example: Torque applied to a disk: τ = (radius)(Force from hand)(sinθ).
Moment of Inertia: Measures how mass is distributed relative to the rotation axis, resisting changes in rotational motion.
Sphere: I = (2/5)·m·r²
Torque Equations:
τ = r·F·sin(θ)
τ = I·α, where α is angular acceleration
Relationship of Angular & Linear:
v = ω·r — Linear velocity from angular velocity and radius.
Summary of Key Equations
2. I = (2/5)·m·r² (Moment of Inertia for Sphere)
3. τ = I·α (Torque Equation)
4. v = ω·r (Linear-Angular Relationship)