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Rotational Kinematics

AP Physics 1· difficulty 4/5

A wheel starts from rest and accelerates uniformly to 30 rad/s30\text{ rad/s} in 5 s5\text{ s}. Through how many revolutions does it turn during this interval?

  • A

    ≈11.9 rev\approx 11.9\text{ rev}

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  • B

    ≈75 rev\approx 75\text{ rev}

  • C

    ≈23.9 rev\approx 23.9\text{ rev}

  • D

    ≈5.0 rev\approx 5.0\text{ rev}

Explanation

θ=12(ω0+ω)t=12(0+30)(5)=75 rad\theta = \tfrac{1}{2}(\omega_0 + \omega)t = \tfrac{1}{2}(0 + 30)(5) = 75\text{ rad}. Then 75/(2π)≈11.9 rev75/(2\pi) \approx 11.9\text{ rev}.

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