The main disk's angular velocity, Ω, is 1 rad/s about the fixed X-Y axes. The rider disk is attached to the main disk 3 meters from the center and has an angular velocity, ω, of 2 rad/s relative to the main disk.
The rotating x-y axes are attached to the main disk and rotate with the main disk.
The rider is 1.5 m from the rider-disk center.
The question requires the velocity at t = 2.4 s. Since both the time and angular velocities are known, the rotational position of both disks can be determined by θ = Ω t and β = ω t. The final position can be determined with θ and β known.
The disks are assumed to be at full speed at
t = 0.0 s. This ignores all start up accelerations (accelerations are examined in the next section).
Use the relative velocity equation in the I-J fixed coordinate system (the i-j system could also be used):
vB = vA + Ω × rB/A + vB/A
Analyze each term in the equation.