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?!!!!

Answer 1

h = 4 sin (314.15 t)

Step-by-step 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)