You are given a gold ingot (thin rectangular sheet, length L, width W, thickness

Question

You are given a gold ingot (thin rectangular sheet, length L, width W, thickness T) of mass M and volume V. You toss it in the air and flip it, so as to make it spin about a symmerty axis that lies in the sheet and is perpendicular to the length. You know how much torque you applied and you can see its angular velocity. So, you conclude that its moment of inertia is (ML^2)/10. You also know that the smelting process was crude and allowed lots of tiny air bubbles to get caught in the gold.

Let's assume that the ingot is pure gold with some air bubbles. In terms of the mass, M, and volume, V, of the ingot, what is the total volume of the air bubbles trapped in the gold ingot?

Explanation / Answer

moment of inertia of the about a symmerty axis that lies in the sheet and is perpendicular to the length of the gold thin rectangular sheet is    I =ML^2/10 if thin rectangular sheet is initially at rest the initial angular speed is   1  = 0 rad/s at time t the angular speed is 2 angular acceleration is    = (2-1)/t                                         = 2/t the required torque applied is   = I*                                                   = (ML^2/10)*2/t ___________________________________________________________________________ for pure gold the volume i.e length of the rectangular sheet and mass of the rectangular sheet are if not changed, then moment of inertia will not chang but density of the pure gold is changed. from above equation   = (ML^2/10)*2/t in this equation no quantities depend on the density there fore in both cases we get same results for same length and same mass. and 2/t value also not depend on density there fore no quantities are affect the above equation for same mass and length we get same results in pure gold case only density will change is not affect the above equation moment of inertia of the about a symmerty axis that lies in the sheet and is perpendicular to the length of the gold thin rectangular sheet is    I =ML^2/10 if thin rectangular sheet is initially at rest the initial angular speed is   1  = 0 rad/s at time t the angular speed is 2 angular acceleration is    = (2-1)/t                                         = 2/t the required torque applied is   = I*                                                   = (ML^2/10)*2/t ___________________________________________________________________________ for pure gold the volume i.e length of the rectangular sheet and mass of the rectangular sheet are if not changed, then moment of inertia will not chang but density of the pure gold is changed. from above equation   = (ML^2/10)*2/t in this equation no quantities depend on the density there fore in both cases we get same results for same length and same mass. and 2/t value also not depend on density there fore no quantities are affect the above equation for same mass and length we get same results in pure gold case only density will change is not affect the above equation angular acceleration is    = (2-1)/t                                         = 2/t the required torque applied is   = I*                                                   = (ML^2/10)*2/t ___________________________________________________________________________ for pure gold the volume i.e length of the rectangular sheet and mass of the rectangular sheet are if not changed, then moment of inertia will not chang but density of the pure gold is changed. from above equation   = (ML^2/10)*2/t in this equation no quantities depend on the density there fore in both cases we get same results for same length and same mass. and 2/t value also not depend on density there fore no quantities are affect the above equation for same mass and length we get same results in pure gold case only density will change is not affect the above equation

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