17. Definition of Angular Velocity
Angular velocity is the rate of change of angular displacement.
ω = Δθ / Δt
Its SI unit is:
rad s⁻¹
Other units include:
- Degrees per second
- Revolutions per second
- Revolutions per minute
18. Average Angular Velocity
Average angular velocity is total angular displacement divided by total time:
ωavg = Δθ / Δt
For rotation at a constant rate, average and instantaneous angular velocities are equal.
19. Instantaneous Angular Velocity
Instantaneous angular velocity is the angular velocity at a particular instant.
ω = lim (Δt → 0) (Δθ / Δt)
Using calculus notation:
ω = dθ / dt
20. Direction of Angular Velocity
Angular velocity points along the axis of rotation.
Its direction is determined using the right-hand rule:
- Curl the right-hand fingers in the rotational direction.
- The thumb indicates the direction of ω⃗.
Angular velocity is not directed along the circular path.
21. Revolutions per Minute
If rotational speed is N revolutions per minute:
1 rev = 2π rad
and:
1 min = 60 s
Therefore:
ω = 2πN / 60
22. Solved Example: RPM to Angular Velocity
Question: A wheel rotates at 120 rpm. Find its angular velocity.
Solution
ω = 2π(120) / 60
ω = 4π
ω = 12.57 rad s⁻¹
Final Answer
ω = 12.57 rad s⁻¹
