Centripetal vs tangential acceleration

Centripetal bends, tangential speeds up. Total acceleration is the vector sum.

Centripetal vs tangential acceleration0 min · Free lecture

In this lesson

  • Centripetal bends, tangential speeds up. Total acceleration is the vector sum.

A car speeding around a curve: the pedal gives tangential, the steering gives centripetal.

a_c = v²/r (radial, always present when turning); a_t = dv/dt = rα (tangential, present when speed changes). Total: a = √(a_c² + a_t²).

Uniform circular motion has a_t = 0; non-uniform has both — the total acceleration points neither along the radius nor the tangent.

a=ac2+at2a = \sqrt{a_c^2 + a_t^2}

Total acceleration in curved motion

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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Centripetal vs tangential acceleration — FemtoLearn.
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Centripetal bends, tangential speeds up. Total acceleration is the vector sum.
Printable notes (free)

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.