Understanding Angular Acceleration and Velocity in Pulley Systems

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SUMMARY

The discussion focuses on calculating angular acceleration and angular velocity in a pulley system with a radius of 3.25 cm and a weight falling with a constant acceleration of 3.10 m/s². The angular acceleration of the pulley is determined to be 95.4 rad/s², derived from the linear acceleration of the weight. Additionally, the angular velocity of the pulley when the weight hits the floor is also calculated to be 95.4 rad/s, leading to a query about the consistency of these results. The equations used include Angular Acceleration = Δω/Δt and Angular Velocity = Δθ/Δt.

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  • Understanding of angular motion equations
  • Familiarity with linear acceleration concepts
  • Knowledge of the relationship between linear and angular quantities
  • Basic physics principles related to pulleys and rotational dynamics
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  • Study the relationship between linear acceleration and angular acceleration in rotational systems
  • Learn how to derive angular velocity from linear displacement
  • Explore the implications of constant acceleration in pulley systems
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of pulley systems and the relationship between linear and angular motion.

mike.yeagley2
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The question I am given is as follows:

A string is wrapped around a pulley of radius 3.25cm, and a weight hangs from the other end. The weight falls with a constant acceleration 3.10m/s^2.

1. What's the angular acceleration of the pulley?
2. If the weight starts from rest 1.55m above the floor, what's the pulley's angular velocity when the weight hits the floor?

My issue is with the equations I have available to me.

Equations: Angular Acceleration=Δω/Δt Angular Velocity=Δθ/Δt w=2pi/t and the equivalent translational versions for the weight in question 2.

I am looking to understand how to formulate the correct equations to get the answer. Any help would be appreciated.
 
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Is that homework?
 
Yes it is. I found the equation I needed for Part one with linear acceleration, and that makes sense. The answer was 95.4rad/s^2, but the answer was the same for the second question as well, and I don't fully understand that. I am looking to understand why it is the same answer.
 

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