A fan blade, initially at rest, rotates with a constant acceleration of 0.020 rad/s2. What is the time interval required for it to reach a 8-rad displacement after starting from rest?Select one:a.40 sb.28 sc.80 sd.0.16 se.20 s
Question
A fan blade, initially at rest, rotates with a constant acceleration of 0.020 rad/s2. What is the time interval required for it to reach a 8-rad displacement after starting from rest?Select one:a.40 sb.28 sc.80 sd.0.16 se.20 s
Solution
To solve this problem, we can use the equation of motion which is:
θ = ω₀t + 0.5αt²
where: θ is the angular displacement, ω₀ is the initial angular velocity, t is the time, α is the angular acceleration.
Given in the problem, we know that: θ = 8 rad, ω₀ = 0 (since the fan blade starts from rest), α = 0.020 rad/s².
Substituting these values into the equation, we get:
8 = 0t + 0.50.020*t² 8 = 0.01t²
Solving for t, we get:
t² = 8 / 0.01 t² = 800 t = sqrt(800) t = 28.28 s
So, the closest answer is b. 28 s.
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