Does the Work-Energy Theorem hold true for objects in rotational motion?

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SUMMARY

The discussion centers on the application of the Work-Energy Theorem to objects in rotational motion, specifically comparing a solid sphere and a cube of equal mass on a frictionless table. It is established that while both objects experience the same linear acceleration due to an equal applied force, the sphere also gains rotational kinetic energy, resulting in a greater total kinetic energy compared to the cube. The conversation clarifies that the work done on the sphere is indeed greater because the point of contact moves faster due to the sphere's rotation, thus resolving the perceived paradox regarding the theorem's applicability.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Familiarity with the Work-Energy Theorem
  • Basic concepts of rotational motion and kinetic energy
  • Knowledge of frictionless surfaces and their implications in physics
NEXT STEPS
  • Study the implications of the Work-Energy Theorem in rotational dynamics
  • Explore the differences between translational and rotational kinetic energy
  • Investigate real-world applications of Newton's laws in rotational systems
  • Learn about torque and its effects on rotational motion
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Physics students, educators, and anyone interested in understanding the principles of rotational motion and energy conservation in mechanics.

  • #31
Fantasist said:
Any reference to support this claim (I mean experimental data)?
This is standard material in any introductory statics class. My textbook was Meriam and Kraige, Statics, V1, 3rd Ed, p. 52-53, but I cannot imagine that any statics text would skip such a basic concept.

As far as experiments go, you can do this one yourself. Just get an air hockey table, apply a tangential force to the puck, and note that the puck translates as well as rotates.

Fantasist said:
There seems to be a kind of circular argument in place here: from a kinematical point of view (according to F=ma), you know the force only if you know the acceleration. But the acceleration is the unknown here (we are trying to figure out whether the sphere will translate or not in a given situation)
According to Newton and everyone since him, the puck will translate and rotate due to an isolated tangential force. According to you it will only rotate.

I fail to see the circular argument, other than the fact that you argue incessantly about anything involving circular motion.
 

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