How Do You Calculate Tension and Angular Acceleration in a Pulley System?

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SUMMARY

The discussion focuses on calculating the tension in a pulley system involving two masses, m1 (10 kg) and m2 (50 kg), and a pulley with a moment of inertia (I) of 60 kg*m² and an inner radius (r) of 1 m. To solve for the tension in the rope and the angular acceleration of the pulley, participants recommend starting with free-body diagrams for each mass. The relationship between linear dynamics and rotational dynamics is emphasized, particularly the role of moment of inertia in the calculations.

PREREQUISITES
  • Understanding of Newton's Second Law for linear motion
  • Familiarity with rotational dynamics concepts, specifically moment of inertia
  • Ability to draw and interpret free-body diagrams
  • Basic knowledge of angular acceleration calculations
NEXT STEPS
  • Study the derivation of tension equations in pulley systems
  • Learn how to apply Newton's Second Law to rotational systems
  • Explore examples of free-body diagrams in mechanics
  • Investigate the relationship between linear acceleration and angular acceleration
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics, particularly those studying dynamics and rotational motion in pulley systems.

Drewbie
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Homework Statement



Two rocks, with masses m1 and m2, are attached to the opposite ends of a rope that runs around the inner radius r of a pulley with moment of inertia I

m1 = 10 kg
m2 = 50kg
I = 60 kg*m^2
r = 1 m

I have to determine Tension for both masses and the angular acceleration of the pulley.

I am aware that moment of inertia is equivalent to mass in linear dynamics, but I don't know how to set up the problem. Any help pointing me in the right direction would be appreciated.
 
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Start by drawing the free-body diagram for each body.
 

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