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7 June, 00:25

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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  1. 7 June, 02:07
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    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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