Cars and trains on curved tracks

Friction supplies the centripetal force on flat curves; banking adds a normal-force component.

Cars and trains on curved tracks0 min · Free lecture

In this lesson

  • Friction supplies the centripetal force on flat curves; banking adds a normal-force component.

Icy curve, fast car: the required centripetal exceeds what friction can give — and the car slides out.

Flat curve: friction f = mv²/r ≤ μmg → v_max = √(μgr).

Banked curve (no friction needed): tanθ = v²/(rg); the 'safe speed' formula. With friction, a range of speeds is safe.

vmax=μgr,tan⁡θ=v2rgv_{max} = \sqrt{\mu g r},\quad \tan\theta = \frac{v^2}{rg}

Flat and banked curve limits

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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Cars and trains on curved tracks — FemtoLearn.
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Friction supplies the centripetal force on flat curves; banking adds a normal-force component.

Frequently asked

Why bank curves?

Banking lets the normal force contribute centripetal force, reducing reliance on friction.

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.