Torque, energy, and average power

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SUMMARY

The discussion focuses on calculating the torque, energy, and average power required to accelerate the Earth from rest to its current angular speed over a period of 3 days. The rotational inertia of the Earth is established as 9.72126 x 10^31 kg*m^2, derived from the formula for a solid sphere. The angular acceleration is calculated as 2.80478 x 10^-10 rad/s², leading to a torque of 2.7266 x 10^22 N*m. Participants emphasize the importance of using correct units and converting the radius of the Earth to meters for accurate calculations.

PREREQUISITES
  • Understanding of rotational dynamics and torque calculations
  • Familiarity with the concept of rotational inertia
  • Knowledge of angular acceleration and its calculation
  • Proficiency in unit conversion, particularly between kilometers and meters
NEXT STEPS
  • Review the derivation of rotational inertia for different shapes, focusing on solid spheres
  • Learn about angular acceleration and its implications in rotational motion
  • Explore the relationship between torque, angular acceleration, and rotational inertia
  • Study unit conversion techniques to ensure accuracy in physics calculations
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Physics students, engineers, and anyone involved in mechanics or rotational dynamics who seeks to deepen their understanding of torque and angular motion calculations.

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Calculate the torque (in N*m), energy (in J), and average power (in W) required to accelerate the Earth in 3 days from rest to its present angular speed about its axis.
 
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t = I*a

rotational inertia of a solid sphere = 2/5*m*r^2
mass of Earth = 5.9742*10^24 kg
radius of Earth = 6378.1 km
rotational inertia of the Earth = 9.72126*10^31

a = delta v / delta t
angular speed of the Earth = 7.27*10^-5 rad/s
3 days = 259200 seconds
a = (7.27*10^-5)/(259200) = 2.80478*10^-10 torque = (9.72126*10^31)*(2.80478*10^-10) = 2.7266*10^22 N*m

But this answer is wrong, I don't know why... please help me. Am I on the right track, am I using the correct equations?
 
rotational inertia of the Earth = 9.72126*10^31

Check this one. Should be ~ 9.7*10^37 kgm^2

Also you have not written the units for some quantities. Units matters.

Gamma.
 
You probably didn't change the radius of the Earth to meters. :)
 

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