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5 June, 04:48

A dentist's drill starts from rest. After 3.00 s of constant angular acceleration it turns at a rate of 2.90 ✕ 10^4 rev/min.

(a) Find the drill's angular acceleration.

(b) Determine the angle (in radians) through which the drill rotates during this period.

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  1. 5 June, 05:09
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    Initial angular velocity wi = 0

    final angular velocity wf = 2.9 x 10⁴ rev/min

    wf = 2.9 x 10⁴ (2*3.14 rad) / (60 sec)

    wf = 3.035 x 10³ rad/sec

    time t = 3 sec

    angular acceleration α

    wf = wi + αt

    3.035 x 10³ = 0 + α (3)

    α = 1012 rad/s²

    (b) angle covered is θ

    θ = wi*t + (1/2) αt²

    θ = 0*3 + (1/2) (1012) (3²)

    θ = 4554 rad
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