A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is its angular speed at the instant it goes through an angular displacement of 7.00 rad? A)280 rad/s B)0.175 rad/s C)0.592 rad/s D)880 rad/s

Question

Quizplus · Accepted Answer

Let's use the kinematic equation: 
θ = ω_i t + 1/2 α t^2
where:
θ = angular displacement = 7.00 rad
ω_i = initial angular speed = 0 rad/s (because it starts from rest)
α = angular acceleration = 0.025 rad/s^2
t = time required to reach the final displacement (which we want to find)

Rearranging and solving for t:
t = sqrt(2θ/α) = sqrt(2*7.00/0.025) = 23.664 s

Finally, we use the kinematic equation:
ω = ω_i + α t
to find the final angular speed:
ω = 0 + 0.025 * 23.664 = 0.592 rad/s

Therefore, the answer is C) 0.592 rad/s.

A Fan Blade,initially at Rest,rotates with a Constant Acceleration of 0.025