For convenience, convert the given speed to rad/s :
20.0rev / 5.00s = 4.00rev / s(2πrad / rev) = 25.1rad / s
So when Dario stops spinning the spinner, it has this angular velocity (ω). Its final angular velocity (ω₀) is zero because it comes to rest. From the time it stops spinning to when it stops it goes through an angle (Δθ) of 6.00rev(2πrad / rev) = 37.7rad. From :
ω² = ω₀² + 2αΔθ
α = (ω² - ω₀²) / 2Δθ
= [(25.1rad/s)² - 0] / (2 x 37.7rad)
= 8.36rad/s²
Hope this makes sense.
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