Angular displacement

Angle swept around the centre, measured in radians — the natural ruler of rotation.

Angular displacement0 min · Free lecture

In this lesson

  • Angle swept around the centre, measured in radians — the natural ruler of rotation.

A full turn is 2π radians, not 360 degrees — radians make every rotation formula clean.

Angular displacement θ = arc length / radius (radians). Positive by convention counterclockwise. θ is a vector along the axis (right-hand rule) in 3D, signed scalar in a plane.

Conversions: 360° = 2π rad; degrees to radians: ×π/180.

θ=sr\theta = \frac{s}{r}

Angle from arc length

Worked example

A car speeds up while turning on a circular track. Its total acceleration:

  1. Speeding up gives tangential acceleration; turning gives radial acceleration.
  2. Total = vector sum of both.

Answer: Is the vector sum of radial and tangential parts

Transcript (0 min)
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Angular displacement — FemtoLearn.
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Angle swept around the centre, measured in radians — the natural ruler of rotation.
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Practice

Free · 4 questions with full solutions
  1. Q1 · MCQ · difficulty 2/5

    A car speeds up while turning on a circular track. Its total acceleration:

    • Points along the radius
    • Points along the tangent
    • Is the vector sum of radial and tangential parts
    • Is zero
  2. Q2 · Numerical · difficulty 1/5

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

  3. Q3 · 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.

  4. Q4 · 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.