Need a relation between W,F,M,KE,P,Imp and H (one relation)

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SUMMARY

The discussion focuses on deriving a single relation among Work (U), Force (F), Moment (M), Kinetic Energy (T), Linear Momentum (Q), Impulse (Imp), and Angular Momentum (H) in the context of mechanics. The user presents various equations, including U1->2 = T2 - T1 and T = (1/2)mv² + (1/2)Iω², to explore connections between these concepts. The attempt at a solution suggests integrating force and momentum equations, indicating a comprehensive approach to the problem. The user seeks validation for their derived equations and relationships.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with equations of motion and energy conservation
  • Knowledge of calculus for integration of force and momentum
  • Basic grasp of angular motion and its equations
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  • Study the derivation of the work-energy theorem in mechanics
  • Learn about the conservation of linear and angular momentum
  • Explore the relationship between impulse and momentum
  • Investigate the principles of rotational dynamics and their equations
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Engineering students, particularly those studying mechanics, as well as educators preparing for exams in classical mechanics and physics. This discussion is beneficial for anyone seeking to understand the interrelations of fundamental mechanical concepts.

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hi I'm in faculty of engineering.. and i study mechanics III .. there's a question that the doctor brought in the exam years ago.. and i couldn't solve it and its probably going to be in the final exam tomorow..

Homework Statement



The question is simply: Find a relation (one relation) between all of those (Work, Force, Moment, kinetic energy, linear momentum, impulse, angular momentum)
the question is like an impossible one !
thnx all

Homework Equations



U:work T:kinetic energy F:force M:moment Imp:impulse Q:linear momentum H:angular momentum ω:angular velocity θ:angle

U1->2 = T2-T1
T = (1/2)mv2 + (1/2)Iω2
U1->2 = ʃ Fdr
rotation motion. U1->2 = Mdθ
Q=mv
Imp1->2 = ʃ Fdt
Imp1->2 = Q2 - Q1
∑ ʃ Mdt = Ho1 - Ho2

The Attempt at a Solution



U1->2 = T2 - T1 = ʃ Fdr = M(θ2 - θ1) = ʃ Qdv

rxImp1-2 = ∑ ʃ Mdt = H2 - H1
 
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this solution is right?
 
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