Question

The disc A is pinned at O and weighs 15lbs. A

1-ft rod weighing 2lbs and a 1-ft diameter sphere
weighing 10lbs are welded to the disc, as shown.
If the spring is originally stretched 1ft and the
sphere is released from the position shown,
determine the angular velocity of the disc when
it has rotated 90 degrees. Assume that the spring wraps
around the disc.

Answer 1

To determine the angular velocity of the disc when it has rotated 90 degrees, we can use the principle of conservation of angular momentum. The initial angular momentum of the system is equal to the final angular momentum of the system.

The initial angular momentum is given by the product of the moment of inertia and the initial angular velocity. The final angular momentum is given by the product of the moment of inertia and the final angular velocity.

Since the spring wraps around the disc, it contributes to the moment of inertia. We need more information about the spring and its properties to calculate the final angular velocity.