A solid, horizontal cylinder of mass 12.2 kg and radius 1.00 m rotates with an angular speed of 6.00 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.

An incident ray through the focal point of a spherical mirror will: reflect through the center of curvature. reflect back through the focal point. reflect parallel to the principle axis. reflect the same direction as the incident ray.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

Classify each possible hypothesis about a medicinal aloe vera plant as falsifiable or non-falsifiable. aloe vera gel is the best natural skin moisturizer. aloe vera gel can heal wounds by boosting cell renewal. aloe vera juice tastes better than carrot juice. drinking aloe juice can reduce the risk of lung cancer.