Question 5 A fidget spinner that is 4 inches in diameter is spinning clockwise. The spinner spins at 3000 revolutions per minute

Question

Question 5
A fidget spinner that is 4 inches in diameter is spinning clockwise. The spinner spins at 3000
revolutions per minute.
At t = 0, consider the point A on the outer edge of the spinner that is along the positive horizontal
axis. Let h(t) be the vertical position of A in inches. Suppose t is measured in minutes. Find a
sinusoidal function that models h(t).
h(t) =

Can someone please help me for this question?!!!!! ASAP?!!!!

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Khoii Minh 6 months 2021-08-13T23:22:37+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-08-13T23:24:15+00:00

    Answer:

       h = 4 sin (314.15 t)

    Explanation:

    This is a kinematics exercise, as the system is rotating at a constant speed.

              w = θ / t

              θ = w t

    in angular motion all angles are measured in radians, which is defined

             θ = s / R

       we substitute

              s / R = w t

              s = w R t

    let’s reduce the magnitude to the SI system

        w = 3000 rev / min (2π rad / 1rev) (1min / 60 s) = 314.16 rad / s

       

    let’s calculate

       s = 314.16 4 t

       s = 1,256.6 t

    this is the value of the arc

    Let’s find the function of this system, let’s use trigonometry to find the projection on the x axis

                      cos θ = x / R

                      x = R cos θ

                      x = R cos wt

    projection onto the y-axis is

                   sin θ = y / R

         

    how is a uniform movement

                   θ = w t

                   y = R sin wt

    In the case y = h

                  h = R sin wt

                  h = 4 sin (314.15 t)

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