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The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t³ - 6t². The torque on the wheel becomes zero at

1. t = 1 s
2. t = 0.5 s
3. t = 0.25 s
4. t = 2 s

Correct answer: t = 1 s

Solution

The torque is proportional to the angular acceleration, which is the second derivative of angular position θ(t) with respect to time. Differentiating θ(t) = 2t³ - 6t² twice, we get angular acceleration α = d²θ/dt² = 12t - 12. Setting α = 0 gives t = 1 s.

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