A gramophone record turntable accelerate from rest to an angular velocity of 45.0 rev per min in 1.60 s. What is its average angular acceleration? (Ans: 2.945 rad s⁻²)



Data Given:


Initial angular velocity = `\à´§_i` = 0 rad s⁻¹

Final angular velocity = `\à´§_f` = 45 rev min⁻¹ = 45ｘ `\frac {2ã„«}{60}` rad s⁻¹ = 1.5ã„« rad s⁻¹ = 1.5ｘ3.1416 rad s⁻¹ = 4.712 rad s⁻¹

Time = t = 1.60 s


To Find:


Angular Acceleration  = ∝ = ?


Solution:


Using formula for angular acceleration ∝

∝ = `\frac {à´§_f - à´§_i}{Δt}`

By putting values

∝ = `\frac {4.712 rad s⁻¹ - 0 rad s⁻¹}{1.6 s}`

∝ = `\frac {4.712 rad s⁻¹}{1.6 s}`

∝ = 2.945 rad s⁻²

or

∝ = 2.945 rad s⁻²



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