A circular disk starts from rest and spins around its central axis until it reaches 10 rad/s in 30 seconds at a constant angular acceleration. What is the angular acceleration?
Divide the final angular velocity (10 rad/s) by the time required to accelerate to that value (30 s). The dimensions of the answer will be rad/s^2
To find the angular acceleration, we can use the formula:
angular acceleration (α) = change in angular velocity (ω) / change in time (t)
Given:
Initial angular velocity (ω0) = 0 rad/s (since the disk starts from rest)
Final angular velocity (ω) = 10 rad/s
Time (t) = 30 seconds
Using the formula, we can calculate the angular acceleration:
α = (ω - ω0) / t
= (10 rad/s - 0 rad/s) / 30 s
= 10 rad/s / 30 s
= 1/3 rad/s²
Therefore, the angular acceleration is 1/3 rad/s².