An object starts to rotate about an axis from rest wih a, uniform angular acceleration of 2pi rads-2 what is the no.of rotations it can comp

Question

An object starts to rotate about an axis from rest wih a, uniform angular acceleration of 2pi rads-2 what is the no.of rotations it can complete in 5s

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Nho 6 months 2021-07-17T03:19:58+00:00 1 Answers 2 views 0

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    2021-07-17T03:21:03+00:00

    Answer:

    θ = 12.5 rotations

    Explanation:

    The number of rotations can be found by using the second equation of motion:

    \theta = \omega_i t + \frac{1}{2}\alpha t^2\\\\

    where,

    \theta = angular displacement = ?

    ωi = initial angular speed = 0 rad/s

    t = time = 5 s

    α = angular acceleration = 2π rad/s²

    Therefore,

    \theta = (0\ rad/s)(5\ s)+\frac{1}{2}(2\pi\ rad/s^2)(5\ s)^2\\\\\theta = 78.54\ rad

    converting it to no. or rotations:

    \theta = (78.54\ rad)(\frac{1\ rotation}{2\pi\ rad})

    θ = 12.5 rotations

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