The 100 kg wheel shown in the figure has a radius of gyration of kG = 0.25 m about its center of mass G. If it is subjected to a clockwise couple of 20 Nm as it rolls on its inner hub without slipping, determine the wheel’s angular velocity after the 20 kg block is released from rest and has fallen 0.4 m. The spring has a stiffness of k = 60 N/m and is initially unstretched when the block is released. Angular velocity is required Principle of work and energy is the most analytic “economical” tool to use. It is easier to analyze the system as a whole than to consider the components separately Position Position Kinetic Energies: Work done Nw and R do not work since they do not move along their lines of action Fr does no work since wheel does not slip as it rolls Wheel does not slip wheel moves through as block moves a distance s such that spring stretches = rD/Ic = (0.4)(0.571) = 0.228 m Principle of Work and Energy:
The 100 kg wheel shown in the figure has a radius of gyration of kG = 0.25 m about its center of mass G. If it is subjected to a clockwise couple of 20 Nm as it rolls on its inner hub without slipping, determine the wheel’s angular velocity after the 20 kg block is released from rest and has fallen 0.4 m. The spring has a stiffness of k = 60 N/m and is initially unstretched when the block is released. Angular velocity is required Principle of work and energy is the most “economical” analytic tool to use. It is easier to analyze the system as a whole than to consider the components separately Position Position Kinetic Energies: Work done Nw and R do not work since they do not move along their lines of action Fr does no work since wheel does not slip as it rolls Wheel does not slip wheel moves through as block moves a distance s such that spring stretches = rD/Ic = (0.4)(0.571) = 0.228 m Principle of Work and Energy:
Ch04%20Kinetics%20of%20particles%20Rigid%20Bodies.docx