Question

An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s.

Answer 1

Answer:

a) -1.25 rev/s² and 23.3 rev

b)  2.67s

Explanation:

a) ω$Ф_o_z$ = (500 rev/min)(1min/ 60s) => 8.333 rev/s

ω$Ф_Z$= (200 rev/min)(1min/ 60s) => 3.333rev/s

time 't'= 4 s

angular acceleration 'α$Ф_Z$'=?

constant angular acceleration equation is given by,

ω$Ф_Z$= ω$Ф_o_z$ + α$Ф_Z$t

α$Ф_Z$= (ω$Ф_Z$ - ω$Ф_o_z$ )/t => (3.333-8.333)/4

α$Ф_Z$= -1.25 rev/s²

θ-θ$Ф_o$ = ω$Ф_o_z$ t + 1/2α$Ф_Z$t²

      =(8.333)(4) + 1/2 (-1.25)(4)²

      =23.3 rev

b) ω$Ф_Z$=0   (comes to rest)

ω$Ф_o_z$ = 3.333 rev/s

α$Ф_Z$= -1.25 rev/s²

ω$Ф_Z$= ω$Ф_o_z$ + α$Ф_Z$t

t= (ω$Ф_Z$ - ω$Ф_o_z$)/α$Ф_Z$ => (0- 3.333)/-1.25

t= 2.67s