A 89.3 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.77 rad/s . A monkey drops a 8.83 kg bunch of bananas vertically onto the platform. They hit the platform at 4 5 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.1 kg , drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.69 m .

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?

How would a small bar magnet be oriented when placed at position x?

A10nc charge sits at a point in space where the magnitude of the electric field is 1500 n/c. what will the magnitude of the field be if the 10 nc charge is replaced by a 20 nc charge? assume the system is big enough to consider the charges as small test charges.