2) The position of a particle is given r(t) = A(cos wt i + sin wt f), where w is a constant. (a) Show that the particle moves in a circle of

Question

2) The position of a particle is given r(t) = A(cos wt i + sin wt f), where w is a constant. (a) Show that the particle moves in a circle of radius A. (b) Calculate and then show that the speed of the particle is a constant. (c) Determine and show that a is given by ac = rw. (d) Calculate the centripetal force on the particle.

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Thiên Hương 5 years 2021-08-18T06:06:11+00:00 1 Answers 38 views 0

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  1. Sigrid
    0
    2021-08-18T06:07:41+00:00
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    Answer:

    Explanation:

    r(t) = A(cos wt i + sin wt f)

    = A cos wt i + A sin wt j

    x = A cos wt

    y = A sin wt

    radius r

    r² = x² + y² ( This is equation of a circle with radius r  )

    =  A² cos² wt +A² sin² wt

    = A²

    r = A

    radius r = A

    b )

    speed = dr/dt

    v = – Aw sinwt i + Aw coswt j

    magnitude of velocity

    I v I= Aw √(sin²wt + cos²wt)

    = Aw ( constant )

    acceleration

    = dv / dt = – Aw² cos wt – Aw² sinwt

    magnitude of acceleration

    I a I = Aw²

    = r w²

    d ) centripetal force = m acceleration

    m w² A  

    =

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