Q6.1 Rotating wheel (S)

The angular position of a reference point on a spinning wheel is given by
θ=2t3-18t+3
where t is in seconds, and θ in radians.
  1. Find the angular speed ω(t)
  2. Find the angular acceleration α(t)
  3. Determine if ω is ever zero.

Solution

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Solution

  1. Differentiating θ w.r.t t we get ω
    ω=6t2-18
  2. Differentiating again we get α
    α=12t
  3. Solving for ω=0 we find the wheel stationary at $t= \pm \sqrt{3}\,s$.