Confused about torque vs. energy (Joules)

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SUMMARY

The discussion clarifies the relationship between torque and energy, specifically in the context of a solid disk with a friction torque of 10 Nm. The energy lost to friction is calculated as 10 Joules, as 1 Joule is equivalent to 1 Nm. The confusion arises from the similarity in units, but the total energy lost due to friction is determined by the torque and the angular displacement, not just the torque value alone. Understanding the rotational work equation, Work = Torque × Angular Displacement, is essential for accurate calculations.

PREREQUISITES
  • Understanding of rotational dynamics
  • Familiarity with the concepts of torque and energy
  • Knowledge of angular displacement in radians
  • Basic grasp of work-energy principles
NEXT STEPS
  • Study the relationship between torque and angular displacement in rotational systems
  • Learn about the work-energy theorem in the context of rotational motion
  • Explore examples of energy loss due to friction in mechanical systems
  • Investigate the implications of friction torque in engineering applications
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Physics students, mechanical engineers, and anyone interested in understanding the principles of rotational dynamics and energy loss in systems involving friction.

johnschmidt
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Homework Statement



Solid disk, 50cm in diameter, with a mass of 5kg. Disk is located in space by a bearing. The friction torque of the bearing is 10Nm. A string is wrapped around the disk and connected to a weight. The weight is allowed to fall and spin the disk. How much energy is lost to friction?

Homework Equations



1 Joule = 1Nm

The Attempt at a Solution



Since the friction torque is 10Nm, the energy lost to friction is 10J (same as 10Nm). Is this right? I'm confused by torque having the same units as Joules...
 
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Do you remember the equation...

work = force (N) * distance (m)

Well the equivalent for rotation is...

Work = torque (in Nm) * angular displacement (in Radians)
 
Even worse for you, the total energy lost due to friction is not the same as the frictional torque. There is a relation between work and the torque and the total angle turned. It is similar to the work resulting from a force translating a certain distance.
 

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