Find the equilibrium position of the winch

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SUMMARY

The discussion focuses on determining the equilibrium position of a winch system involving a whip with a specific moment of inertia (I), a crank of length (l) and mass (m), and a hoist with mass (m). The key objective is to balance the torques around the rotation axis, specifically analyzing the torque contributions from the hanging mass and the crank. The analysis requires understanding the dynamics of the system while ignoring resistance movement, leading to insights on the oscillation cycle following small positional changes of the crank.

PREREQUISITES
  • Understanding of torque and rotational dynamics
  • Familiarity with moment of inertia concepts
  • Knowledge of equilibrium conditions in mechanical systems
  • Basic principles of oscillatory motion
NEXT STEPS
  • Study the principles of torque in rotational systems
  • Learn about calculating moment of inertia for various shapes
  • Explore equilibrium conditions in mechanical engineering
  • Investigate oscillation cycles and their mathematical modeling
USEFUL FOR

Mechanical engineers, physics students, and anyone involved in the design or analysis of winch systems and rotational dynamics.

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Homework Statement


A whip made from a material shaped shaft axis radius R and moment of inertia I and a crank with the axis perpendicular to the axis of rotation of length l and mass m, while the rest parallel to the handle - mass ##m_{2}##. It hangs on a hoist that has mass m. Suppose rope hanging objects weighing negligible.

Homework Equations


Find the equilibrium position of the winch (ie alpha angle on the picture) and the oscillation cycle of generation after small changes of the crank position. Ignore the resistance movement.

The Attempt at a Solution


Please explain for me how to do it, thank and sorry my bad English

anh11.PNG
 
Physics news on Phys.org
In equilibrium, the torques about the rotation axis have to balance. What is the torque from the hanging mass? What is the torque from the crank and the handle?
 

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