A particle makes 240 revolution per minute on a circular radius of 2m find: (1) it’s period (2) it’s angular velocity (3) it’s linear veloci

Question

A particle makes 240 revolution per minute on a circular radius of 2m find: (1) it’s period (2) it’s angular velocity (3) it’s linear velocity (4) it’s acceleration

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Nick 5 years 2021-08-01T19:28:09+00:00 1 Answers 668 views 1

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  1. sori
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    2021-08-01T19:29:41+00:00
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    Answer:

    (1) The period 0.25 secs

    (2) The angular velocity is 25.14 rad/s

    (3) The linear velocity is 50.28 m/s

    (4) The acceleration is 1264 m/s^{2}

    Explanation:

    (1) Period is defined as the time taken for one revolution

    ∴ Period = \frac{Time }{Number of revolutions }

    From the question, the particle makes 240 revolution per minute

    That is, For 240 revolution, the time taken = 1 minute

    Time = 1 minute = 60 secs

    Number of revolutions = 240

    ∴ Period =\frac{60}{240} \\

    Period = 0.25 secs

    The period 0.25 secs

    (2) The angular velocity, ω is given by

    ω = \frac{2\pi }{T} \\

    where T is the period

    ∴ω = 2 ×\frac{22}{7} / 0.25           (take \pi = \frac{22}{7})

    ω = 25.14 rad/s

    The angular velocity is 25.14 rad/s

    (3) The linear velocity, v is given by

    v = ωr

    Where v is the linear velocity

    ω is the angular velocity

    and r is the radius

    From the question, r = 2m

    From v = ωr

    ∴v = 25.14 × 2

    v = 50.28 m/s

    The linear velocity is 50.28 m/s

    (4) The acceleration is given by

    a = ω × v = ω(ωr) =ω²r

    ∴ a = 25.14^{2} × 2

    a = 1264.04 m/s^{2} \\a = 1264 m/s^{2}

    The acceleration is 1264 m/s^{2}

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