Answer:
a) 65.2 s
b) -0.083 rad/s/s
c) 19 s
Explanation:
a) Angular displacement = θ = 28 rev = 28 × 2 π =175.9 rad
Initial angular velocity = ω₁ = 5.4 rad/s
Final angular velocity = ω₂ = 0, since it comes to rest
Angular acceleration = α = ( ω₂² - ω₁² ) / 2θ = - 0.083 rad/s/s
Time taken to come to rest = t = (ω₁ - ω₁ ) / α = 65.2 s
b) Angular acceleration = α = - 0.083 rad/s/s
c) Angular displacement = θ ' = 14 rev = 87.96 rad
θ'= ω₁ t + 0.5 α t²
Angular acceleration is said to be constant.
⇒ 87.96 = 5.4 t + 0.5 ( - 0.083 ) t²
⇒ 0.0415 t² - 5.4 t + 87.96 = 0
Solving this quadratic equation for t,
⇒ t =111 s or 19 s
(Since time for 28 rev is 65.2 s, for 14 rev , it cannot be greater than that so 19 s is chosen out of the two roots for t)
