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)
