A 2kg hollow sphere with a 30cm diameter is welded onto a thin 5kg rod that is 1.3m in length to form a hybrid scepter-staff for a narcissistic king. The king will often balance it in his palm with the sphere up and then let it fall over and swing down. What is the difference in linear speed of the center of mass and the outer edge of the sphere when the staff-scepter is at the bottom?
At what angle from the vertical does the weld have to accelerate the sphere faster than gravity?

Aplane takes off from an airport and flies to town a, located d1 = 215 km from the airport in the direction 20.0° north of east. the plane then flies to town b, located d2 = 230 km at 30.0° west of north from town a. use graphical methods to determine the distance and direction from town b to the airport. (enter the distance in km and the direction in degrees south of west.)

Which lists the main components of darwin’s theory of evolution? a. random mutations drive evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms do not change. b. natural selection drives evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms change over time. c. natural selection drives evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms change over time. d. random mutations drive evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms do not change.

Which of the following best describes internal energy? a. the difference between the kinetic and potential energies of the particles in a system b. the sum of the kinetic and potential energies of the particles in a system c. the sum of the kinetic and thermal energies of the particles in a system d. the difference between the kinetic and thermal energies of the particles in a system