Two horizontal rods are each held up by vertical strings tied to their ends. Rod 1 has length L and mass M; rod 2 has length 2L and mass 2M. Each rod then has one of its supporting strings cut, causing the rod to begin pivoting about the end that is still tied up. Which rod has a larger initial angular acceleration?A Rod 1 B. Rod 2 C. The initial angular acceleration is the same for both.

Rod 1 has greater initial angular acceleration; The initial angular acceleration for rod 1 is greater than for rod 2.

Explanation:

For the rod 1 the angular acceleration is

Similarly, for rod 2

Now, the moment of inertia for rod 1 is

,

and the torque acting on it is (about the center of mass)

therefore, the angular acceleration of rod 1 is  

Now, for rod 2 the moment of inertia is

and the torque acting is (about the center of mass)

therefore, the angular acceleration is

We see here that

therefore

In other words , the initial angular acceleration for rod 1 is greater than for rod 2.

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