![]() ![]() However, the teacher later gave the explanation that the dumbbell would in fact increase in speed as when the handle was rotating, the weights would be rotating at the same speed and thus when it impacts, the weights which have larger circumference would have the same rotations/min as the handle (which has a smaller circumference) and thus as it is larger, with the same rotation rate, would increase speed. "If I have a dumbbell that is rolling down an incline with only its handle rolling (the weights are hanging off the sides of the incline), what would happen to it's speed when it tocuhes the ground and keeps rolling? Does it increase, decrease or stay constant?"Īt first I thought the answer was simple, it would decrease in speed as it would expend energy during its impact with the ground (I don't think this is a valid reason though). (Public Domain Maschen).As in the title, our Physics teacher gave us this brain teaser after learning introductory motion. Since the rod is rigid, the position of the bob is constrained according to the equation f(x,y)=0, the constraint force is C, and the one degree of freedom can be described by one generalized coordinate (here the angle theta). I am slightly reminded of this when discussing Hamilton’s principle in dynamics ![]() We calculate the virtual work done and set it to zero. When using the principle of virtual work in statics we imagine starting from an equilibrium position, and then increasing one of the coordinates infinitesimally. 13.9: Hamilton's Variational Principle Hamilton’s variational principle in dynamics is slightly reminiscent of the principle of virtual work in statics.13.8: More Lagrangian Mechanics Examples More examples of using Lagrangian Mechanics to solve problems.Thus any conclusions that we reach about our soap will also be valid for a pendulum. ![]() Note also that this is just the same constraint of a pendulum free to swing in three-dimensional space except that it is subject to the holonomic constraint that the string be taut at all times. that it remains in contact with the basin at all times.
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