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A student on a piano stool is rotating freely with an angularspeed of 3.05 rev/s

ID: 1724746 • Letter: A

Question

A student on a piano stool is rotating freely with an angularspeed of 3.05 rev/s. the student holds a 1.50 kg mass in eachoutstretched arm, 0.759m from the axis of rotation. The combinedmoment of inertia of the student and the stool, ignoring the twomasses is 5.53 kg m^2, a value that remains constant. A) As the student pulls his arms inward, his angular speedincreases to 3.69 rev/s. How far are the masses from the axis ofrotation? B)What is the final and inital KE of the system? A student on a piano stool is rotating freely with an angularspeed of 3.05 rev/s. the student holds a 1.50 kg mass in eachoutstretched arm, 0.759m from the axis of rotation. The combinedmoment of inertia of the student and the stool, ignoring the twomasses is 5.53 kg m^2, a value that remains constant. A) As the student pulls his arms inward, his angular speedincreases to 3.69 rev/s. How far are the masses from the axis ofrotation? B)What is the final and inital KE of the system?

Explanation / Answer

I1 = 5.53 + 2(1.5)(0.759)^2
   = 7.2582kgm^2
According to conservation of angular momentum
   I22 =I11   
     I2= I11   /  2   
   I2 = 7.2582(3.05) /3.69
   = 5.9993
  So moment of inertia is
   5.53 + 2(1.5)R^2 =5.9993
   R = 0.3955m
------------------------------------------------------------------------------------------------
  initial KE
   Ki =(1/2)I112
   = 33.759J
  Final kinetic energy
   Kf =(1/2)I222
   = 40.8435J      
   = 40.8435J