A wheel rotating with uniform angular acceleration covers 50 rev in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

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(1) $2 π rad / s^{2}, (10 π) rad / s$

(4) $4 πrad / s^{2}, (30 π) rad / s$

(3) $(8 π) r a d / s^{2}, (40 π) rad / s$

(2) 5 $π rad / s^{2},$ $(20 π) rad / s$

answer is C.

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Detailed Solution

$θ = \frac{1}{2} {αt}^{2} ∴ α = \frac{2 θ}{t^{2}} = \frac{2 (50) (2 π)}{(5)^{2}} = (8 π) rad / s^{2} = 25.14 rad / s^{2} ω = (αt) = (8 π) (5) = (40 π) rad / s$

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