An ant is following a circular pheromone trail. The ant takes 14 s to complete one ‘lap’ and is moving at a speed of 8.5 cm s−1. What is the radius of the pheromone trail?
What is the angular velocity of the ant?

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.

Which statements describe how a machine can make work easier? check all that apply. it can put out more force than the input force by decreasing the distance through which force is applied. it can increase the amount of work performed if the output force is in the same direction as the input force. it can apply a force to an object in a different direction than the force applied to the machine. it can increase the distance through which a force acts by exerting less force than was used on it. it can exert a greater force through a greater distance than the force used on the machine.

What is the momentum of an 85 kg runner traveling at 8 m/s?