The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 2.00 s. How long does it take door B (also starting from rest) to rotate through the same angle?
To determine the time it takes for door B to rotate through the same angle as door A, we can use the principle of rotational motion. The principle states that the rotational acceleration of an object is directly proportional to the torque applied and inversely proportional to the object's moment of inertia.
In this scenario, both doors are uniform and identical, so we can assume that they have the same moment of inertia. The only difference is their axis of rotation. Door A rotates about its left edge, while door B rotates about its center.
Since the same force is applied perpendicular to each door at its right edge, the torque applied to each door is the same. This means that the rotational accelerations of both doors are equal. Therefore, we can conclude that the time it takes for door B to rotate through the same angle as door A will also be the same.
In other words, the time for door B to rotate through the same angle would also be 2.00 s.