Asolid uniform disk with a mass m and a radius r is pivoted around a horizontal axis through its center, and a small object with mass m is attached to the rim of the disk. if the disk is released from rest with the small object at the end of a horizontal radius, find the angular velocity of the small object at the bottom.

Ametal ring 4.20 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. these magnets produce an initial uniform field of 1.12 t between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.240 t/s . (a) what is the magnitude of the electric field induced in the ring? (b) in which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?