Figure shows a uniform disk, with mass M = 2.5 kg and radius R = 20 cm, mounted on a fixed horizontal axle. A block with mass m = 1.2 kg hangs from a massless cord that is wrapped around the rim of the disk. Find the acceleration of the falling block, the angular acceleration of the disk, and the tension in the cord. The cord does not slip, and there is no friction at the axle.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Analyze the Forces on the Block
The block of mass \( m \) is subjected to two forces: the gravitational force \( mg \) acting downward and the tension \( T \) in the cord acting upward. According to Newton's second law, the net force acting on the block can be expressed as:
\[ mg - T = ma \]
where \( a \) is the acceleration of the falling block.
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