Final answer:
To find the angular acceleration at t = 2.0 s for the given turntable, we differentiate the angular velocity function and evaluate at t = 2.0 s, the angular acceleration at t = 2.0 s is -10.16 rad/s².
Step-by-step explanation:
To find the angular acceleration at t = 2.0 s, we need to differentiate the given angular velocity function with respect to time. So, the angular acceleration, α(t), is the derivative of ω(t).
Given that ω(t) = 4.5 + 0.64t - 2.7t2, we can differentiate it using the power rule for derivatives.
Taking the derivative, we get α(t) = 0.64 - 5.4t.
Substituting t = 2.0 s into the equation, we find
α(2.0) = 0.64 - 5.4(2.0) = 0.64 - 10.8 = -10.16 rad/s².