How is the torsional rigidity of a shaft mathematically represented_______________?
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Answer: D. torque required to produce a twist of one radian per unit length of shaft
Explanation
Torsional rigidity is defined mathematically as the torque required to produce a twist of one radian per unit length of the shaft. This mechanical property combines the shear modulus of the material with the polar moment of inertia. Higher torsional rigidity ensures that drive shafts twist minimally under high torque transmission loads. Torsion formulas govern the rotational twisting behavior of cylindrical shafts subjected to applied moments. Rigidity calculations differ from strength calculations, focusing on angular deflection rather than fracture limits. Shaft cross-sectional geometry heavily influences torsional rigidity due to the polar moment of area.
Automotive drive shafts require sufficient torsional rigidity to transmit engine power smoothly without excessive wind-up. Precision machine tool spindles must resist twisting to maintain accurate angular synchronization during machining. Engineers analyze torsional stiffness to prevent harmful resonance vibrations in high-speed rotating machinery. Maximum torque capacity refers to the ultimate strength limit of a shaft before structural failure occurs. Number of cycles before failure measures fatigue endurance rather than static torsional rigidity characteristics. Maximum power transmitted at high speeds depends on torque and rotational velocity rather than angular twist per unit length.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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