a) 500 RPM works out to ω = 2π 500/60 = 50π/3 rad/s. The vector direction is along the axis of rotation and, according to the right-hand-rule, pointing away from the viewer observing clockwise rotation.
α = Δω/Δt = (-50π/3)/(2.60 s) ~~ -20.1 rad/s²
The negative sign means that the angular acceleration vector is directed opposite to the original angular velocity vector, along the axis of CD rotation but toward the viewer.
b)
The acceleration is in the opposite direction to the velocity {the disc is slowing down} so the acceleration should be a = -20.1 rad/s² when you plug it in eq. 1-
θ = 52.36 * 2.6 + ½ * (-20.1) * 2.6² = 68.2 rad {rounding errors}
There are 2π radians in 1 revolution, so 68.2 rad / 2π = 10.83 revolutions
That's 10 complete revolutions plus a bit!
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