Answer:
Explanation:
<u>Circular Motion </u>
Suppose there is an object describing a circle of radius r around a fixed point. If the relation between the angle of rotation by the time taken is constant, then the angular speed is also constant. If that relation increases or decreases at a constant rate, the angular speed is given by:
Where is the angular acceleration and t is the time. If the object was instantly released from the circular path, it would have a tangent speed of:
We have two reels: one loaded with the tape to play and the other one empty and starting to fill with tape. They both rotate at different angular speeds, one is increasing and the other is decreasing as the tape goes from one to the other. We'll assume the tangent speed is constant for both (so the tape can play correctly). Let's call the angular speed of the loaded reel and
that from the empty reel. We have
If is the radius of the reel when it's full of tape, the angular speed for the loaded reel is computed by
The tangent speed is computed by knowing the length of the tape and the time needed to fully play it.
If is the radius of the reel when it's empty, the angular speed for the empty reel is computed by
The full reel goes from to
in 6480 seconds, so we can compute the angular acceleration:
The empty reel goes from to
in 6480 seconds, so we can compute the angular acceleration:
So the equations for both reels are
They will be the same when
Solving for t
The common angular speed is
They both result in the same, as expected