Angular Velocity Calculator
This angular velocity calculator shows how fast an angle changes with time. Example: 3000 revolutions per minute correspond to 50 Hz and ω = 100·π ≈ 314.159 rad/s.
Example: What is given: Rotational speed (rpm) · Rotational speed n 3,000 rpm → Result: ω = 314.159 rad/s · 3,000 rpm · f = 50 Hz. Source: Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Rotation“ (ω = Δθ/Δt, ω = 2πf, v = ωr). Updated: .
How it is calculated
Angular velocity ω tells you what angle a rotating body sweeps per unit of time. It is usually given in radians per second (rad/s) and links rotational speed, frequency, period and the speed of a point on the circular path.
Formulas
From the angle: ω = Δφ / Δt, with φ in radians (180° = π rad). From frequency: ω = 2π·f. From rotational speed n in rpm: ω = 2π·n / 60. From linear speed: ω = v / r. The period is T = 2π / ω = 1 / f.
Worked example
A motor runs at 3000 revolutions per minute. That is f = 50 Hz, so ω = 2π · 50 = 100·π ≈ 314.159 rad/s and a period of T = 0.02 s. If a pointer turns through 90° in 2 seconds, ω = (π/2) / 2 = π/4 ≈ 0.7854 rad/s.
- A point 2 m from the axis at ω = 5 rad/s has a linear speed v = ω·r = 10 m/s.
- One full revolution equals 2π ≈ 6.2832 rad or 360°.
- The calculator assumes uniform rotation; for changing speed the value is only an average.
Frequently asked questions
How do you convert rpm to rad/s?
Use ω = 2π·n / 60. At 3000 rpm this gives 100·π ≈ 314.159 rad/s.
How are angular velocity and linear speed related?
Through the radius: v = ω·r. At the same ω, outer points move faster than inner ones.
What is the difference between frequency and angular velocity?
Frequency counts revolutions per second in Hz, angular velocity the angle in radians per second. They are linked by ω = 2π·f.
Sources and legal basis
- Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Rotation“ (ω = Δθ/Δt, ω = 2πf, v = ωr)
- Wikipedia – Winkelgeschwindigkeit
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