Just looking for confirmation for a torque calculation

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SUMMARY

The forum discussion centers on confirming a torque calculation for rotating a 10 mm cube weighing 7.5 grams by 180 degrees in 0.001 seconds. The initial energy calculation presented was 0.0000617 Joules, which was deemed low by participants. Key points include the necessity of torque for rotation, the importance of defining the moment of inertia, and the impact of acceleration profiles on energy requirements. The discussion emphasizes that optimizing torque application can significantly reduce energy expenditure, potentially by a factor of four compared to constant acceleration.

PREREQUISITES
  • Understanding of torque and its role in rotational motion.
  • Familiarity with moment of inertia calculations.
  • Knowledge of kinematic equations for rotational motion.
  • Basic principles of energy conservation in mechanical systems.
NEXT STEPS
  • Study the kinematic equation for rotational motion: $$\Delta \theta=\dfrac{\omega_0+\omega_f}{2}\Delta t$$.
  • Learn about moment of inertia and its calculation for different geometries.
  • Explore optimization techniques for torque application in mechanical systems.
  • Investigate the relationship between angular velocity and energy requirements in rotational dynamics.
USEFUL FOR

Mechanical engineers, physics students, and anyone involved in the design or analysis of rotating systems will benefit from this discussion.

  • #61
jbriggs444 said:
The correct formula is ##KE = \frac{1}{2} \times I \times {\omega_f}^2##

Note that the ##\omega_f## is squared.

If you do not apply the factor of ##\frac{1}{2}## and do not square ##\omega_f## then the result will be angular momentum. We use the symbol "L" for angular momentum: ##L = I \times \omega_f##.


In the car problem, the same applies. The correct formula is ##KE = \frac{1}{2} \times m \times v^2##

If you do not apply the factor of ##\frac{1}{2}## and do not square ##v## then the result will be momentum. We use the symbol "p" for momentum: ##p = m \times v##
Notes taken thank you
 

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