What is the path of the ball's movement in different scenarios?

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SUMMARY

The discussion focuses on the dynamics of a ball with radius r and mass m entering a stationary semispherical shell with radius R, under various conditions of motion. Specifically, it examines three scenarios: (A) the ball's movement when both the car and shell are stationary, (B) the ball's trajectory when the shell rotates about its z-axis with a constant angular velocity w1, and (C) the ball's path when the shell rotates with angular velocity w1 while the car moves in a circular path with angular velocity w2. The coefficient of friction µ between the ball and the shell is also a critical factor influencing the ball's movement.

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  • Understanding of classical mechanics principles, including Newton's laws of motion.
  • Familiarity with rotational dynamics and angular velocity concepts.
  • Knowledge of frictional forces and their impact on motion.
  • Basic grasp of kinematics in circular motion.
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  • Study the effects of friction on rolling motion in physics.
  • Learn about angular momentum and its conservation in rotating systems.
  • Explore the equations of motion for objects in circular paths.
  • Investigate the dynamics of non-inertial reference frames and their effects on motion.
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Physics students, mechanical engineers, and anyone interested in the dynamics of motion in rotating systems will benefit from this discussion.

sina_mech
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hi friends , please help me to solve this problem , THANKS :

A ball with radius r and mass m with angel 30 with horizon and with velocity V, according to figure, enters to a semispherical shell with radius R and the coefficient of friction between semispherical shell and ball is µ . This semispherical shell is in the Car moving at the circular path with radius a .assume that the semispherical shell is without any linear or lateral movement on the car:

A: assume that the velocity of car and the semispherical shell is zero, and determine the path of the Ball’s movement.

B: assume that the semispherical shell rotate about its z-axe with constant angular velocity of w1 and determine the path of the Ball’s movement.

C: assume that the semispherical shell rotate about its z-axe with angular velocity of w1, and the car moves in circular path with constant angular velocity of w2. Determine the path of the Ball’s movement.
 

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