Discussion
That drive reaches 100 rad/s from rest in
Answer: D
Correct answer: 25 s
With constant accelerating torque the acceleration is constant, so
\[ t = \frac{\omega}{d\omega/dt} = \frac{100}{4} = 25 \ \mathrm{s} \]equivalently \( J\omega/(T - T_l) = 10 \times 100/40 \). Twenty-five seconds is a long run-up, and it reflects a large inertia against a modest torque margin - doubling the motor torque would cut it to ten seconds.
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