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AP Physics C: Mechanics
6.2 Torque and Work
6.1 Rotational Kinetic Energy
AdvancedMCQMathematical19.6k
Four identical rigid rotors, initially at rest, each rotate from \(\theta = 0\) to \(\theta = \Theta\) under the influence of a net torque \(\tau(\theta)\), where \(\tau_0\) is a positive constant. The torque functions for the four rotors are given in the table.

RotorNet Torque \(\tau(\theta)\)
1\(\tau_0 \sqrt{\dfrac{\theta}{\Theta}}\)
2\(\tau_0 \left(\dfrac{\theta}{\Theta}\right) | Rotor 1 | \(\tau_0 \sqrt{\dfrac{\theta}{\Theta}}\)
2\(\tau_0 \left(\dfrac{\theta}{\Theta}\right) | Rotor | Net Torque \(\tau(\theta)\)
------
1\(\tau_0 \sqrt{\dfrac{\theta}{\Theta}}\)
2\(\tau_0 \left(\dfrac{\theta}{\Theta}\right)\)
3\(\tau_0 \left(\dfrac{\theta}{\Theta}\right)^2\)
4\(\tau_0 \left[1 - \left(\dfrac{\theta}{\Theta}\right)^2\right]\)

Which of the following correctly ranks the rotational kinetic energies \(K_1\), \(K_2\), \(K_3\), and \(K_4\) of the rotors when they reach \(\theta = \Theta\)?

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