Torque and angular momentum for a Particle in a Force Field

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SUMMARY

The discussion focuses on calculating torque and angular momentum for a particle in a force field defined by the vector function F=(3t^2 -4t)i + (12t -6)j + (6t - 12t^2)k. Participants confirm that the correct approach involves equating r''=F, followed by computing the cross product r X F to determine torque and r X v for angular momentum. It is emphasized that initial conditions, specifically r(0)=(0,0,0) and r'(0), are crucial for solving the differential equations at t=3.

PREREQUISITES
  • Understanding of vector calculus and cross products
  • Familiarity with differential equations and their solutions
  • Knowledge of torque and angular momentum concepts
  • Basic principles of classical mechanics
NEXT STEPS
  • Study the method for solving second-order differential equations
  • Learn about the properties of torque and angular momentum in three-dimensional space
  • Explore the application of initial conditions in solving mechanical problems
  • Investigate the implications of force fields on particle motion
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Students and professionals in physics, particularly those focusing on classical mechanics, as well as engineers and researchers dealing with particle dynamics in force fields.

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[SOLVED] Torque and angular momentum for a Particle in a Force Field

Find A) the torque and B) the angular momentum about the origin at the time t=3 for a particle in a Force Field F=(3t^2 -4t)i + (12t -6)j + (6t - 12t^2)k. Assuming that t=0 is located at the origin.


I equated r"=F then took r X F is this the proper way? Then took r X v to find angular momentum. Any help would be appreciated.
 
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Yes, that's the right way. Solve the differential equation r''=F and find v and r at t=3. You not only need to assume r(0)=(0,0,0), you need some initial condition for r'(0). Is it also (0,0,0)?
 
Thanks for the confirmation
 

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