To understand the concept of reactance (of an inductor) and its frequency dependence.

when an inductor is connected to a voltage source that varies sinusoidally, a sinusoidal current will flow through the inductor, its magnitude depending on the frequency. this is the essence of ac (alternating current) circuits used in radio, tv, and stereos. circuit elements like inductors, capacitors, and resistors are linear devices, so the amplitude i0 of the current will be proportional to the amplitude v0 of the voltage. however, the current and voltage may not be in phase with each other. this new relationship between voltage and current is summarized by the reactance, the ratio of voltage and current amplitudes, v0, and i0: xl=v0/i0, where the subscript l indicates that this formula applies to an inductor.

a. to find the reactance xl of an inductor, imagine that a current i(t)=i0sin(? t), is flowing through the inductor. what is the voltage v(t) across this inductor?

express your answer in terms of i0, ? , and the inductance l.

American eels (anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders 1.0 m long and 10 cm in diameter. an eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could. 1.a field researcher uses the slow-motion feature on her phones camera to shoot a video of an eel spinning at its maximum rate. the camera records at 120 frames per second. through what angle does the eel rotate from one frame to the next? 2. the eel is observed to spin at 14 spins per second clockwise, and 10 seconds later it is observed to spin at 8 spins per second counterclockwise. what is the magnitude of the eels average angular acceleration during this time? 3. the eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. if it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning? 4.a new species of eel is found to have the same mass but one-quarter the length and twice the diameter of the american eel. how does its moment of inertia for spinning around its long axis compare to that of the american eel?

Avery hard rubber ball (m = 0.5 kg) is falling vertically at 4 m/s just before it bounces on the floor. the ball rebounds back at essentially the same speed. if the collision with the floor lasts 0.05 s, what is the average force exerted by the floor on the ball?

Which sound characteristic is not affected by the relative motion of an object