Rotational Motion – Stage 1 (Page 2)

Angular Velocity, Angular Acceleration & Relations

After understanding angular displacement, the next step is to define how fast a body rotates and how that rotation changes with time. These ideas are the backbone of all rotational motion problems.

1. Angular Velocity (ω)

Angular velocity is the rate of change of angular displacement with time.

Mathematical form:
ω = dθ / dt

• SI unit: rad s⁻¹
• Vector quantity
• Direction given by Right-Hand Thumb Rule

Key Point: In pure rotation, all particles have the same angular velocity.

2. Direction of Angular Velocity

Curl the fingers of your right hand in the direction of rotation. The thumb gives the direction of angular velocity.

✔ Clockwise and anticlockwise rotations have opposite directions of ω.

3. Angular Acceleration (α)

Angular acceleration is the rate of change of angular velocity with time.

Mathematical form:
α = dω / dt

• SI unit: rad s⁻²
• Vector quantity

4. Uniform Angular Acceleration

If angular acceleration is constant, equations of rotational motion become similar to linear motion.

ω = ω₀ + αt
θ = ω₀t + ½αt²
ω² = ω₀² + 2αθ

Exam Tip: These formulas are valid only for constant α.

5. Relation Between Linear & Angular Quantities

For a particle at distance r from the axis:

Linear velocity: v = rω
Tangential acceleration: a_t = rα

Radial (centripetal) acceleration: a_r = rω²

6. Physical Meaning (Very Important)

✔ Angular velocity is same for all particles
✔ Linear velocity increases with distance from axis
✔ Points near axis move slowly, far points move faster

⚠ Common Mistakes to Avoid

❌ Using v = rω without checking r
❌ Mixing tangential and radial acceleration
❌ Forgetting direction of ω and α

IIT-JEE Insight

Most IIT problems test whether students understand why v changes with r even when ω is constant.

Next: Stage 1 – Page 3
Torque – Concept, Definition & Physical Meaning

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