The fan starts rotating with a constant angular acceleration ε = 0.3 rad / s2 and 15 s after the start of rotation

| March 11, 2021 | education

The fan starts rotating with a constant angular acceleration ε = 0.3 rad / s2 and 15 s after the start of rotation it acquires an angular momentum L = 30 kg * m2 / s. Find the kinetic energy of the fan 20 seconds after the start of rotation.

Data: ε (constant angular acceleration of the considered fan) = 0.3 rad / s2; t1 (first rotation time) = 15 s; L (fan moment of impulse after time t1) = 30 kg * m2 / s; t2 (second rotation time) = 20 s.

1) Find the moment of inertia of the fan in question: L = J * ω1 = J * ε * t1, from where we express: J = L / (ε * t1) = 30 / (0.3 * 15) = 6.67 kg * m2.

2) We calculate the kinetic energy after 20 s: Ek = J * ω2 ^ 2/2 = J * (ε * t2) ^ 2/2 = 6.67 * (0.3 * 20) ^ 2/2 = 120 J.

Answer: After 20 s, the kinetic energy of the fan in question will be equal to 120 J.



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