benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 10094 / An airplane propeller, of moment of inertia I, is subject to the driving torque…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

An airplane propeller, of moment of inertia I, is subject to the driving torque N = N_0 (1 + \alphacos\omega_0t), and a frictional torque due to air resistanceN_f= -b\texttheta ֹ . Find its steady state motion.

category

physics

options

  1. exttheta = exttheta_0 + (b / I)t + [lphaN_0 / (I \omega_0^2 + b \omega_0^3)][I\omega_0sin\omega_0t + b cos \omega_0t]
  2. exttheta = exttheta_0 + (N_0 / b)t + [lphaN_0 / (I^2 \omega_0^3 + b^2 \omega_0)][I\omega_0cos\omega_0t - b sin \omega_0t]
  3. exttheta = exttheta_0 + (b / N_0)t + [lphaN_0 / (I^2 \omega_0^2 + b \omega_0^3)][b cos \omega_0t - I\omega_0sin\omega_0t]
  4. exttheta = exttheta_0 + (b / N_0)t + [lphaN_0 / (I^2 \omega_0^3 + b^2 \omega_0)][b sin \omega_0t - I\omega_0cos\omega_0t]
  5. exttheta = exttheta_0 + [lphaN_0 / (I \omega_0 + b^2 \omega_0^2)][b sin \omega_0t - I\omega_0cos\omega_0t]
  6. exttheta = exttheta_0 + (N_0 / I)t + [lphaN_0 / (I \omega_0^2 + b^2 \omega_0)][I\omega_0cos\omega_0t + b sin \omega_0t]
  7. exttheta = exttheta_0 + (I / N_0)t + [lphaN_0 / (b \omega_0^2 + I \omega_0^3)][I\omega_0sin\omega_0t - b cos \omega_0t]
  8. exttheta = exttheta_0 + (N_0^2 / b)t + [lpha / (I \omega_0^3 + b^2 \omega_0^2)][b sin \omega_0t - I\omega_0cos\omega_0t]
  9. exttheta = exttheta_0 + (N_0 / b)t + [lphaN_0 / (I^2 \omega_0^3 + b^2 \omega_0)][b sin \omega_0t - I\omega_0cos\omega_0t]
  10. exttheta = exttheta_0 + (N_0 / I)t + [lphaN_0 / (b^2 \omega_0^3 + I^2 \omega_0)][b sin \omega_0t - I\omega_0cos\omega_0t]

src

stemez-Mechanics

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
10094
task_id
b3f6b05d-0fde-5b19-a066-72df28723334
task_key
default--test--10094
task_revision_id
1
config / split
default / test

Official source

initial import