Answer:
α = -9.67 rad/s²
Explanation:
the magnitude of the angular acceleration of the wheel can be calculated using the expression below;
ω² = ω₀² + 2α(θ- θ₀)..............eqn(1)
ω² = ω₀² + 2αΔθ...............eqn(2)
Δθ= θ- θ₀= 15.6 rad
ω = 13.5 rad/s
ω₀ = 22.0 rad/s
where ω₀= initial angular velocity
ω= final angular velocity
We can now input all the parameters into the equation(2) above
(13.5)² = (22.0)² + 2αΔθ
2αΔθ= (13.5)² - (22.0)²
2αΔθ= 182.25 - 484
2αΔθ=301.75
But our Δθ= 15.6 rad
2α *15.6 rad = 301.75
2α=301.75/15.6
2α=19.343
α=9.67
the magnitude of the angular acceleration of the wheel is 9.67 rad/s²
