Solve Torque Problem Set N) For Total Kinetic Energy

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SUMMARY

The discussion centers on calculating the total kinetic energy of a rotating system involving a person on a frictionless swivel chair and two 5lb weights. The system is modeled as a cylinder with a diameter of 35cm and a length of 1 meter, having a uniform density of 1 g/cm³. The initial rotation speed is set at 1 revolution per second. The kinetic energy remains constant even when the weights are extended 1 meter from the axis of rotation, demonstrating the conservation of energy in rotational dynamics.

PREREQUISITES
  • Understanding of rotational dynamics and kinetic energy calculations
  • Familiarity with the concepts of centripetal acceleration and tension in rotating systems
  • Knowledge of angular velocity and its conversion to radians per second
  • Basic principles of mass distribution in rigid body rotation
NEXT STEPS
  • Study the equations for rotational kinetic energy and their applications
  • Learn about centripetal force and its role in maintaining circular motion
  • Explore the relationship between angular velocity and linear velocity in rotating systems
  • Investigate the effects of mass distribution on the dynamics of rotating bodies
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This discussion is beneficial for physics students, mechanical engineers, and anyone interested in understanding the principles of rotational motion and energy conservation in dynamic systems.

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N) Cody sits on a frictionless swivel chair(as in the lecture hall). He rests two 5lb weights,which can be approximated as point masses, on his lap (near the axis of rotation) and pushes off to spin the assembly with a rotation speed of 1 revolution per second. Approximate the person and chair combination as a cylinder 35cm in diameter, 1 meter in length with a uniform density of 1 g/cm3. What is the total kinetic energy in this rotating system?
O) He then extends his arms to hold the 5lb weights,1 meter to his left and right as in the demo. Assume that the distribution of masses in the person and chair combination does not change by extending the arms (ie massless arms), only the position of the two 5lb point masses. What is the time for 1 rotation with this distribution of masses.
P) Make a sketch and indicate the angular vector. Indicate the magnitude in rad/sec.
Q) How much tension in the arms here leads to this centripetal acceleration of the masses. R) Show that the total kinetic energy in this rotating system is the same as in N).
 
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