A 106 kg sculpture hangs from a horizontal rod that serves as a pivot about which the sculpture can oscillate. The sculpture's moment of inertia with respect to the pivot is 9.54 kg·m2, and when it is swung at small amplitudes, it is found to oscillate at a frequency of 0.816 Hz. How far is the pivot from the sculpture's center of mass?

Which statement is true? a. kepler's laws apply only to the motion of earth. b. kepler's laws can be used to predict eclipses. c. kepler's laws are true for a central force that is directly proportional to distance. d. kepler's laws can be deduced from newton's laws of motion and gravity.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r