Kinematics gives a different answer?.

Question

An object starts rotating 200° in 5 seconds,finding angular acceleration, two methods i have tried:

ω=Δθ/Δt=200°/5=40deg/s,a=Δω/Δt=40/5=8deg/s^2

Second method:

Δθ=1/2(ωi+ωf)Δt, 200°=(1/2) (0+ωf)5,ωf=80deg/s,a=80/5=16deg/s^2

Which answer is correct and why?

Answer 1

The question lacks clarity.

But this is for certain that the 1st method is not correct.

Because the first formula ( ω=Δθ/Δt ) calculates average angular velocity. For acceleration we need final and initial velocity.

Second method is correct. Because you calculated final angular velocity from the total angular displacement Δθ and time. Then you calculated acceleration from the change in angular velocity from rest ( initial angular velocity is zero) to the final angular velocity.

Answer 2

I assume the object started from rest, and rotated at a constant angular acceleration α to an angle of 200° over a 5s time interval. You can use the relation

Δθ(t) = ω₀t + αt²/2

t = 5s

ω₀ = 0 (started from rest)

The relation simplifies to

Δθ(t) = αt²/2 ⇒

α = 2Δθ(t) / t²

Plug in conditions for t=5s and get

α = 2(100°) / (5s)² = 8 deg/s²