Answer:
a) -1.25 rev/s² and 23.3 rev
b) 2.67s
Explanation:
a) ω[tex]Ф_o_z[/tex] = (500 rev/min)(1min/ 60s) => 8.333 rev/s
ω[tex]Ф_Z[/tex]= (200 rev/min)(1min/ 60s) => 3.333rev/s
time 't'= 4 s
angular acceleration 'α[tex]Ф_Z[/tex]'=?
constant angular acceleration equation is given by,
ω[tex]Ф_Z[/tex]= ω[tex]Ф_o_z[/tex] + α[tex]Ф_Z[/tex]t
α[tex]Ф_Z[/tex]= (ω[tex]Ф_Z[/tex] - ω[tex]Ф_o_z[/tex] )/t => (3.333-8.333)/4
α[tex]Ф_Z[/tex]= -1.25 rev/s²
θ-θ[tex]Ф_o[/tex] = ω[tex]Ф_o_z[/tex] t + 1/2α[tex]Ф_Z[/tex]t²
=(8.333)(4) + 1/2 (-1.25)(4)²
=23.3 rev
b) ω[tex]Ф_Z[/tex]=0 (comes to rest)
ω[tex]Ф_o_z[/tex] = 3.333 rev/s
α[tex]Ф_Z[/tex]= -1.25 rev/s²
ω[tex]Ф_Z[/tex]= ω[tex]Ф_o_z[/tex] + α[tex]Ф_Z[/tex]t
t= (ω[tex]Ф_Z[/tex] - ω[tex]Ф_o_z[/tex])/α[tex]Ф_Z[/tex] => (0- 3.333)/-1.25
t= 2.67s
a) The motor decelerates at a rate of [tex]\frac{5}{4}[/tex] revolutions per square second.
b) A time of 6.667 seconds is required for the fan to come to rest.
a) Let suppose that the electric fan decelerates uniformly. The angular aceleration experienced by the fan ([tex]\alpha[/tex]), in radians per square second, is described below:
[tex]\alpha = \frac{\omega-\omega_{o}}{t}[/tex] (1)
Where:
If we know that [tex]\omega_{o} = \frac{25}{3}\,\frac{rev}{s}[/tex], [tex]\omega = \frac{10}{3} \,\frac{rev}{s}[/tex] and [tex]t = 4\,s[/tex], then the angular acceleration experienced by the motor is:
[tex]\alpha = \frac{\frac{10}{3}\,\frac{rev}{s}-\frac{25}{3}\,\frac{rev}{s}}{4\,s}[/tex]
[tex]\alpha = -\frac{5}{4}\,\frac{rev}{s^{2}}[/tex]
The motor decelerates at a rate of [tex]\frac{5}{4}[/tex] revolutions per square second.
b) The time taken by the motor to come to rest is described by the following kinematic equation:
[tex]t = \frac{\omega - \omega_{o}}{\alpha}[/tex] (2)
If we know that [tex]\omega_{o} = \frac{25}{3}\,\frac{rev}{s}[/tex], [tex]\omega = 0 \,\frac{rev}{s}[/tex] and [tex]\alpha = -\frac{5}{4}\,\frac{rev}{s^{2}}[/tex], then the time taken by the motor is:
[tex]t = \frac{0\,\frac{rev}{s}-\frac{25}{3}\,\frac{rev}{s}}{-\frac{5}{4}\,\frac{rev}{s^{2}} }[/tex]
[tex]t = 6.667\,s[/tex]
A time of 6.667 seconds is required for the fan to come to rest.
We kindly invite to check this question on uniform accelerated motion: https://brainly.com/question/12920060
