Question

a dental drill accelerates from rest to 900 rpm in 2s. what is the angular acceleration ?how many revolution does it make in coming to full speed ​

Answer 1

angular acceleration = 15π rad/s² and number of revolution = 15

A dental drill accelerates from rest to 900 rpm in 2s. we have to find angular acceleration.

angular acceleration, α = change in angular velocity/time taken

= (900rpm - 0)/2s

= (900 × 2π/60 rad/s)/2s

= 900 × π/60 rad/s²

= 15π rad/s²

now we have to find number of revolution.

using formula, ω² = ω_0² + 2αθ

⇒(900rpm)² = 0² + 2 × 15π × θ

⇒(900 × 2π/60)² = 30πθ

⇒(900π²) = 30πθ

⇒θ = 30π

so number of revolution = θ/2π

= 30π/2π = 15 rev

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Answer 2

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angular acceleration = 15π rad/s² and number of revolution = 15. A dental drill accelerates from rest to 900 rpm in 2s.