Why Does the Ball Lag Behind the Falling Board at Angles Less Than 35.3 Degrees?

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The discussion centers on a physics demonstration involving a ball on a board hinged at one end, where the board is elevated at an angle theta. It is established that when the board is released, the ball lags behind due to the differing accelerations of the board's end and its center of mass. The calculated accelerations are 3/2g for the end of the beam and 3/4g for the center of mass, indicating that the angle of elevation influences the ball's lag. The critical angle of 35.3 degrees is highlighted as the threshold below which the ball will consistently lag behind the falling board. The conversation emphasizes the relationship between the board's angle and the resulting motion of the ball.
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problem: a common demonstration, consists of a ball resting at one end of a uniform board of length =L, hinged at the other end, and elevated at an angle theta. a light cup is attached to the board at a distance d from the hinge so that it will catch the ball when the support stick is suddenly removed, which means that d=Lcos(theta) show that the ball will lag behind the falling board when theta is less than 35.3 degrees.

ive found the free acceleration of the end of the beam and the center of mass of the beam which are 3/2g and 3/4g respectively but am not sure where to go from there??
 
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Shouldn't the acceleration at the end of the board depend on the angle of elevation?
 

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