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Describe qualitatively what happens to the system of Fig. if the disk is given an initial clockwise angular velocity as it is released. What changes, if any, occur in the linear acceleration of the block, or the angular acceleration of the disk? See Sample Problem 9-10.

Describe qualitatively what happens to the system of Fig. if the disk is given an initial clockwise angular velocity as it is released. What changes, if any, occur in the linear acceleration of the block, or the angular acceleration of the disk? See Sample Problem 9-10.
 

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
The figure below shows the system containing the disk and block. Assume that the initial clockwise angular velocity of the disk is ω .

236-1072_1.PNG
The upward linear velocity of the block is given as:
v = Rω
Therefore the block initially move upwards with velocity v, however, the forces on the block accelerates the disk lately.
It is important to note that the block does not experiences any initial acceleration from the disk and any change in velocity appears because of the forces experienced by the block. Therefore, the acceleration of the block can be written using the free body diagram given below as:
236-1401_1.PNG
a = mg – T, a
Here mg is the weight of the block, T is the tension in the string and a is the linear acceleration of the block.
Also, the tension in the string provides the angular acceleration to the disk, which can be written using the free body diagram of given below as:

236-2414_1.PNG
236-1083_1.PNG
Here I is the moment of inertia of the disk, and a is its angular acceleration.
One can see from the equations above that the terms involved are similar to what there were in sample problem 9-10. Therefore there will be no change in the linear acceleration of the block and the angular acceleration of the disk.

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