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 4.2 rad? A) 0.025 rad/s B) 0.11 rad/s C) 0.46 rad/s D) 1.2 rad/s

Question

Quizplus · Accepted Answer

Using the angular kinematic equation, 
θ = ω_i*t + (1/2)*α*t^2

where θ is the angular displacement, ω_i is the initial angular speed (which is zero), α is the constant angular acceleration, and t is time.

We want to find ω_f, the final angular speed when θ = 4.2 rad. Rearranging the equation and plugging in the given values,

ω_f = sqrt(2*α*θ) 
= sqrt(2*0.025 rad/s^2 * 4.2 rad) 
= 0.46 rad/s

Therefore, the answer is C) 0.46 rad/s.

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