Answer:
A. α = - 1.047 rad/s²
B. θ = 14.1 rad
C. θ = 2.24 rev
Explanation:
A.
We can use the first equation of motion to find the acceleration:
[tex]\omega_f = \omega_i + \alpha t[/tex]
where,
ωf = final angular speed = 0 rad/s
ωi = initial angular speed = (30 rpm)(2π rad/1 rev)(1 min/60 s) = 3.14 rad/s
t = time = 3 s
α = angular acceleration = ?
Therefore,
[tex]0\ rad/s = 3.14\ rad/s + \alpha(3\ s)[/tex]
α = - 1.047 rad/s²
B.
We can use the second equation of motion to find the angular distance:
[tex]\theta = \omega_it +\frac{1}{2}\alpha t^2\\\theta = (3.14\ rad/s)(3\ s) + \frac{1}{2}(1.04\ rad/s^2)(3)^2[/tex]
θ = 14.1 rad
C.
θ = (14.1 rad)(1 rev/2π rad)
θ = 2.24 rev
