turntable cart

Atwood's machine ] bag of marbles ] balance moon stone ] ball up/down ] bead parabola accelerometer ] boat anchor lake ] boat time ] bobbin on incline ] bosun's chair ] bouncing ball ] bowling ball rolling ] bug on band ] bursting shell ] falling chain ] Feynman's restaurant problem ] five pills ] flying cable ] forced pendulum ] gold mountain ] half pills ] hallway pole ] impelled rod ] inelastic relativistic collision ] infinite pulleys ] mass on an incline ] maximum angle of deflection ] packs of shirts ] particle in bowl ] particle in cone ] particle on sphere ] particle points parabola ] pile of bricks ] pion muon neutrino ] piston ramp spring ] plank weight trough ] rocket vs. jet ] roll without slipping ] rough inclined plane ] shooting marbles ] speedometer test ] three balls ] three logs ] [ turntable cart ] two rolling balls ] wheel and block ] whirling pendulum ] worlds fair ornament ]

service

 

A turntable of moment of inertia I0 rotates freely on a hollow vertical axis. A cart of mass m runs without friction on a straight radial track on the turntable. A cord attached to the cart passes over a small pulley and then downward through the hollow axis. Initially the entire system is rotating at angular speed ω0, and the cart is at a fixed radius R from the axis. The cart is then pulled inward by applying an excess force to the cord, and eventually arrives at radius r, where it is allowed to remain.

a)      What is the new angular velocity of the system?

b)      Show in detail that the difference in the energy of the system between the two conditions is equal to the work done by the centripetal force.

 c)      If the cord is released, with what radial speed, dr/dt, will the cart pass the radius R?

Answer


Solutions (listed by author)

Michael A. Gottlieb (pdf, 81K)

 

Copyright 2000-2013 Michael A. Gottlieb. All rights reserved.