PhysicsLAB AP Free Response Question
1999 C3

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As shown above, a uniform disk is mounted to an axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disk so that it will rotate with the disk. A block is attached to the end of the rod. Properties of the disk, rod, and block are as follows.
 
 
The system is held in equilibrium with the rod at an angle  to the vertical, as shown above, by a horizontal string of negligible mass with one end attached to the disk and the other to a wall. Express your answers to the following in terms of m, R, , and g.
 
 (a) Determine the tension in the string.

The string is now cut, and the disk-rod-block system is free to rotate.
 
(b) Determine the following for the instant immediately after the string is cut.
 
 i. The magnitude of the angular acceleration of the disk.

 ii. The magnitude of the linear acceleration of the mass at the end of the rod

As the disk rotates, the rod passes the horizontal position shown below.
 
 
 (c) Determine the linear speed of the mass at the end of the rod for the instant the rod is in the horizontal position.




 
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