Period, frequency and rpm

T = 2π/ω, f = 1/T, ω = 2πf = 2π·rpm/60 — the clock of circular motion.

Period, frequency and rpm0 min · Free lecture

In this lesson

  • T = 2π/ω, f = 1/T, ω = 2πf = 2π·rpm/60 — the clock of circular motion.

300 rpm sounds fast until you convert: ω = 2π×300/60 = 10π rad/s.

One revolution is 2π radians: ω = 2π/T = 2πf. rpm → rad/s: multiply by 2π/60.

The unit-conversion trap (rpm vs rad/s) is the single most common error in circular questions.

ω=2πf=2πT=2π⋅rpm60\omega = 2\pi f = \frac{2\pi}{T} = \frac{2\pi \cdot \text{rpm}}{60}

Angular frequency conversions

Worked example

In uniform circular motion, the acceleration of the particle is directed:

  1. Speed is constant but velocity direction changes continuously.
  2. The change in velocity points toward the centre → centripetal acceleration a_c = v²/r toward the centre.

Answer: Toward the centre of the circle

Transcript (0 min)
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Period, frequency and rpm — FemtoLearn.
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T = 2π/ω, f = 1/T, ω = 2πf = 2π·rpm/60 — the clock of circular motion.
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Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 1/5

    A wheel rotates at 270 rpm. What is its angular velocity in rad/s?

  2. Q2 · Numerical · difficulty 1/5

    A point is at distance 1.7 m from the axis of a wheel rotating with angular velocity 11 rad/s. Find its linear speed.

  3. Q3 · Numerical · difficulty 2/5

    A particle moves on a circle of radius 1.5 m with constant speed 6 m/s. Find the magnitude of its centripetal acceleration.

  4. Q4 · MCQ · difficulty 1/5

    In uniform circular motion, the acceleration of the particle is directed:

    • Along the tangent to the circle
    • Toward the centre of the circle
    • Away from the centre of the circle
    • It is zero