Final answer:
The magnitude of the initial tangential acceleration of end b can be determined by considering the change in tangential velocity and the change in radius when the string on side b is retied with half the length.
Step-by-step explanation:
To determine the initial tangential acceleration of end b, we need to consider the relationship between the tangential velocity and the centripetal acceleration. In this scenario, the string on side a has a certain tangential velocity, and it is retied on side b with half the length. The magnitude of the initial tangential acceleration of end b will depend on the change in tangential velocity and the change in radius.
Since the length of the string on side b is now half of the string on side a, we can infer that the radius on side b would also be half of the radius on side a. Therefore, the magnitude of the initial tangential acceleration of end b would be half of the magnitude of the initial tangential acceleration of end a.
For example, if the initial tangential acceleration of end a is 5 m/s^2, the initial tangential acceleration of end b would be 2.5 m/s^2.