How Long Does It Take a Rolling Spool to Hit the Floor?

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SUMMARY

The discussion centers on calculating the time it takes for a solid cylindrical spool, with a mass of 9.4 kg and a radius of 0.11 m, to hit the floor from a height of 9.06 meters under the influence of gravity (9.8 m/s²). The original approach involved equating torque and moment of inertia but yielded incorrect results. A suggested alternative method is to apply energy conservation principles to relate speed and height, potentially allowing for integration to determine height versus time.

PREREQUISITES
  • Understanding of rotational dynamics, specifically torque and moment of inertia.
  • Familiarity with kinematic equations for linear motion.
  • Knowledge of energy conservation principles in physics.
  • Ability to perform integration in the context of motion equations.
NEXT STEPS
  • Study the principles of rotational dynamics, focusing on torque and moment of inertia calculations.
  • Learn how to apply energy conservation in mechanical systems, particularly in rolling motion.
  • Explore the integration of motion equations to derive time from height in free-fall scenarios.
  • Review examples of similar problems involving rolling objects to solidify understanding.
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Physics students, educators, and anyone interested in solving problems related to rotational motion and energy conservation in mechanics.

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"A string is wound around a solid cylindrical spool of mass 9.4 kg and radius .11 m. Assume the acceleration of gravity to be 9.8 m/s^2. If the spool is released from rest and rolls along the string and the distance to the floor is 9.06 meters, then how long in seconds will it take the spool to hit the floor?"

I'm having trouble solving this. I tried setting torque equal to torque r*m*g=moment of inertia*(a/r). After I solved for acceleraton I threw it into the linear kinematics equation 9.06=.5*a*t^2 to solve for time ..but it didn't work out so well because I got the wrong answer. Am I thinking about this incorrectly? What other method can I use?

Thanks all for your help.

Diagram seen below:

http://portfolio.iu.edu/whoblitz/rotationalproblem.PNG
 
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Have you considered using energy conservation? That would tell you speed versus height which you may be able to integrate and find height versus time.
 

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