A playground merry-go-round with a mass of 105 kg and a radius of 1.4m is rotating with an angular frequency of 0.42 rev/s. What is the magnitude of its angular velocity in radians per second, after 17kg child gets onto it by grabbing its outer edge?

Your target variable is δf, the magnitude of the difference in frequency between the waves emitted from the sonar device and the waves received by the device after reflecting off the whale. write an expression for δf in terms of the relevant frequencies using the subscript notation introduced above.

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?

Abumper car with a mass of 250 kg is traveling at a speed of 4 m/s. this bumper car collides and sticks to a second bumper car with a mass of 250 kg, which is initially at rest. what is the final speed of these two bumper cars after the collision, assuming they remain stuck together?