A 0.19-m radius grinding wheel takes 2.8 s to speed up from 3.0 rad/s to 12.0 rad/s. What is the wheel's average angular acceleration?Select one:a.6.4 rad/s2b.3.2 rad/s2c.16.9 rad/s2d.1.1 rad/s2e.0.6 rad/s2
Question
A 0.19-m radius grinding wheel takes 2.8 s to speed up from 3.0 rad/s to 12.0 rad/s. What is the wheel's average angular acceleration?Select one:a.6.4 rad/s2b.3.2 rad/s2c.16.9 rad/s2d.1.1 rad/s2e.0.6 rad/s2
Solution
The average angular acceleration can be calculated using the formula:
α = Δω / Δt
where: α is the average angular acceleration, Δω is the change in angular velocity, and Δt is the change in time.
Given: Initial angular velocity (ω1) = 3.0 rad/s, Final angular velocity (ω2) = 12.0 rad/s, Change in time (Δt) = 2.8 s.
We can calculate the change in angular velocity (Δω) as:
Δω = ω2 - ω1 Δω = 12.0 rad/s - 3.0 rad/s Δω = 9.0 rad/s.
Now we can substitute Δω and Δt into the formula to find α:
α = Δω / Δt α = 9.0 rad/s / 2.8 s α = 3.2 rad/s².
So, the wheel's average angular acceleration is 3.2 rad/s². The correct answer is b. 3.2 rad/s².
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