A rigid disk is rotating with a constant angular velocity of w. There is a smooth...

 

  

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A rigid disk is rotating with a constant angular velocity of w. There is a smooth groove on the disk that allows free motion of a particle along the radial direction of the disk. At t-0, a particle with a mass m is placed in the groove with a distance to the center of ro. The particle has no initial velocity along the radial direction. No need to consider gravity. Determine the following parameters as a function of time t (>0): (1) The radial velocity of the particle. (Hint: recall 2nd order ODE) (2) The lateral force acting on the particle, which is exerted by the wall of the groove. ro 3 A rigid disk is rotating with a constant angular velocity of w. There is a smooth groove on the disk that allows free motion of a particle along the radial direction of the disk. At t-0, a particle with a mass m is placed in the groove with a distance to the center of ro. The particle has no initial velocity along the radial direction. No need to consider gravity. Determine the following parameters as a function of time t (>0): (1) The radial velocity of the particle. (Hint: recall 2nd order ODE) (2) The lateral force acting on the particle, which is exerted by the wall of the groove. ro 3