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Linear and Angular Momentum of Three Small Balls

Newbie

Linear and Angular Momentum of Three Small Balls

By D.M. Griffin, Jr.

linear_and_angular.png

  • Calculate the speed, relative speed, and energy loss of a system, consisting of three small spheres connected to a small ring by three separate cords 
  • Apply to Physics, Academia, and PTC Mathcad usage 
  • Perform using linear velocity, speed, relative speed, linear momentum, angular momentum, energy loss, etc.

     This worksheet looks at three small spheres of equal mass that are connected to a small ring by three inextensible, inelastic cods of equal length and equal space. The spheres can slide freely on a frictionless horizontal surface and rotate at a linear velocity when the cord CD breaks. After the two cords become taught again, this worksheet determines the speed of the ring, the relative speed at which spheres A and B rotate about D, and the fraction of the energy in the original system which is lost when AD and BD become taught. To begin, the worksheet presents you with several diagrams of the relevant system and notes that there are no external forces or moments acting on the system and that linear and angular momentum are conserved just after CD breaks until the system reaches a new equilibrium state. 

     The worksheet then conducts calculations for the linear momentum of masses A and B after cord CD breaks, but before the system reorients itself. It also calculates for the linear moment after the cord between A and B becomes taut again. One those calculations have been achieved, the worksheet shows you how to conduct calculations for the angular momentum about point D immediately after the cord breaks and before the system adjusts, the angular momentum about the new center of mass, D, located between the two remaining balls, and the angular momentum relative to the spheres, about the same point as before D, after the cords have become taught again. After that, the worksheet shows you how to calculate for energy loss.

     This worksheet provides you with images, formulas, calculations, notation, and solutions to aid you with your own calculations.

     Download and explore this worksheet yourself! You can download a free lifetime copy of PTC Mathcad Express and get 30 days of full functionality.