The entrance of a science museum features a funnel into which marbles are rolled one at a time. The marbles circle around the wall of the funnel, eventually spiraling down into the neck of the funnel. The internal radius of the funnel at the top is 0.50 m. At the bottom, the funnel’s neck narrows to an internal radius of 0.041 m. A 5.5 × 10−2 kg marble begins rolling in a large circular orbit around the funnel’s rim at 0.27 rev/s. If it continues moving in a roughly circular path, what will the marble’s angular speed be as it passes through the neck of the funnel? (Consider only the effects of conservation of angular momentum.) Answer in units of rad/s.

Four objects are being tested to see how they are affected by fluid friction. object w has a surface area of 4.5 cm2, object x has a surface area of 2.5 cm2, object y has a surface area of 6.2 cm2, and object z has a surface area of 3 cm2. which object would experience the most fluid friction?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

What conclusion can be made based on the temperature of soil when the light hits the soil at 0°, 45°, and 90° angles in section 2 of the experiment? did your results support your hypothesis? why or why not?