a disk initially at rest rotates with constant angular acceleration through an angel of 50 rad in 5 sec find the angular speed of the disk just after 3 sec. please step by step

Recall the formula,

∆θ = ω₀ t + 1/2 α t ²

where ∆θ = angular displacement, ω₀ = initial angular speed (which is zero because the disk starts at rest), α = angular acceleration, and t = time. Solve for the acceleration with the given information:

50 rad = 1/2 α (5 s)²

α = (100 rad) / (25 s²)

α = 4 rad/s²

Now find the angular speed ω after 3 s using the formula,

ω = ω₀ + α t

ω = (4 rad/s²) (3 s)

ω = 12 rad/s

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