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

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The discussion focuses on analyzing the movement of a ball with specific parameters as it interacts with a semispherical shell under various conditions. In scenario A, where both the car and shell are stationary, the ball's trajectory can be determined based on gravitational and frictional forces. Scenario B introduces rotation of the shell, requiring an examination of how angular velocity affects the ball's path. In scenario C, the combined effects of the shell's rotation and the car's circular motion complicate the analysis further. The participants seek assistance in solving these physics problems related to motion dynamics.
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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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