Circular kinematics problems

The solving recipe: convert to radians, list θ-ω-α-t, use the rotational SUVAT, then bridge with v = rω.

Circular kinematics problems0 min · Free lecture

In this lesson

  • The solving recipe: convert to radians, list θ-ω-α-t, use the rotational SUVAT, then bridge with v = rω.

Circular kinematics is linear kinematics with Greek letters — same recipe.

1) Convert all angles to radians and speeds to rad/s. 2) List θ₀, ω₀, α, t. 3) Apply the rotational equations. 4) Convert back to linear quantities at the requested radius.

The rpm trap and the radius trap are the two killers — check units twice.

θ=ω0t+12αt2\theta = \omega_0 t + \tfrac12 \alpha t^2

Rotational kinematics

Worked example

A disc's angular position is θ = 2t² rad. Find its angular velocity at t = 3 s.

  1. ω = dθ/dt = 4t.
  2. At t = 3: ω = 12 rad/s.

Answer: 12

Transcript (0 min)
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Circular kinematics problems — FemtoLearn.
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The solving recipe: convert to radians, list θ-ω-α-t, use the rotational SUVAT, then bridge with v = rω.
Printable notes (free)

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 disc's angular position is θ = 2t² rad. Find its angular velocity at t = 3 s.

  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.