Class notes on Rotational motion

Best Notes on Rotational Motion
by Anindya Saha




1. Introduction
Rotational motion occurs when an object rotates about a fixed axis. Unlike linear motion,
all points move in circular paths around the axis. Examples: spinning wheel, Earth’s
rotation, ceiling fan, merry-go-round.


2. Angular Quantities
Linear motion ↔ Rotational motion equivalents:
• Displacement → Angular displacement (θ, radians)
• Velocity → Angular velocity (ω, rad/s)
• Acceleration → Angular acceleration (α, rad/s2 )
• Mass → Moment of inertia (I, kg·m2 )
• Force → Torque (τ , N·m)

2.1 Angular Displacement
s
θ=
r

2.2 Angular Velocity
dθ
ω= , v = rω
dt

2.3 Angular Acceleration
dω
α= , at = rα
dt

3. Rotational Kinematics (constant α)
ω = ω0 + αt
θ = ω0 t + 12 αt2
ω 2 = ω02 + 2αθ
(ω+ω0 )
θ= 2
t

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