How can there be work due to torque?

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SUMMARY

The discussion centers on the concept of work done by torque in rotational motion, specifically addressing the equation W = TΔΘ. It clarifies that while torque (T) and the angular displacement (ΔΘ) are perpendicular, work can still be done in rotational systems. This contrasts with linear motion, where perpendicular forces do not contribute to work. The explanation emphasizes understanding the relationship between torque and the distance moved by the force in a rotating shaft.

PREREQUISITES
  • Understanding of rotational dynamics and torque
  • Familiarity with the equation W = TΔΘ
  • Basic knowledge of linear motion and work-energy principles
  • Concept of angular displacement and its relation to rotational motion
NEXT STEPS
  • Study the relationship between torque and angular displacement in detail
  • Explore examples of work done by torque in various rotational systems
  • Learn about the implications of torque in engineering applications
  • Investigate the differences between linear and rotational work-energy principles
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Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to clarify concepts related to torque and work in rotational systems.

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Homework Statement


I'm doing rotational problems and I'm having a hard time understanding how work done by torque is possible.

Homework Equations

The Attempt at a Solution


The equation is W = TΔΘ. Torque points along the axis of rotation and ΔΘ always points along the rotational motion of the object. These two are perpendicular to each other so how can there be work done? I know in linear motion, if the force is perpendicular to the motion of the object, there is no work done. Do these rules not apply to work done on rotating object?
 
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Go back to basics, work is force times distance moved, now look at where the force is in torque and how far it moves when a shaft is spinning.
 
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