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?

   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)

0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2