People riding the spinning-disk ride at Fun Time, Inc. are complaining about high accelerations. An investigation found that the maximum acceleration was occurring at 2.4 seconds.

What is known:

• The main disk rotates at Ω = 1 rad/s (θ = Ωt).
• The rider disk rotates at ω = 2 rad/s (β = ωt).
• Both angular velocities are constant.
• Both disks have no angular acceleration (dω/dt = 0, dΩ/dt = 0).

What is the acceleration of the rider at 2.4 seconds and is it unsafe?

• Use the relative acceleration equation for rotating coordinates,
  
  a_B = a_A + dΩ/dt × r_B/A + Ω × (Ω × r_B/A) 
              + 2 Ω × v_B/A + a_B/A