Dynamics · Physics

Pulley Systems

Connected bodies share constraints. Learn to write equations for each mass and solve them together.

This topic includes

Subtopics to master

Start with ideal strings and pulleys, then solve Atwood machines and multi-body systems.

Tension
Tension in Ideal Strings
Ideal strings are massless and inextensible, so tension is transmitted cleanly.
  • Same tension in a segment
  • Direction along string
  • Constraints between motions
Start subtopicAssumptions matter.
Models
Ideal vs Non-Ideal Pulleys
Non-ideal pulleys can have friction and rotational inertia (intro concept).
  • Ideal pulley assumptions
  • What changes if non-ideal
  • When you can ignore
Start subtopicKnow the simplifications.
Classic
Atwood Machine
Two masses connected over a pulley: derive a and T using FBDs + ΣF=ma for each mass.
  • Two FBDs
  • Constraint: same |a|
  • Solve simultaneous equations
Start subtopicMust-know system.
Systems
Multiple-Object Systems
More than two objects means more equations and constraints (and careful sign choices).
  • Separate FBDs per object
  • Shared accelerations
  • Solving strategy
Start subtopicScale up your method.
Method
Applying Newton’s Laws to Connected Bodies
Write ΣF equations for each body and use constraints to link unknown accelerations.
  • Unknowns list
  • Constraint equations
  • Consistency checks
Start subtopicGeneral framework.
Practice
Practice & Exercises
Pulley drills from Atwood basics to multi-body equation solving.
  • Atwood acceleration and tension
  • Sign convention practice
  • Multiple-object systems
  • Incline + pulley combos
  • Exam-style multi-step sets
Open practiceEquations become routine.