Chapter 9, Problem 9.5P

One of the curators at the art museum is tilting a large cylinder backward. At what angle q will the cylinder of height h and radius r be in unstable equilibrium?

Consider a flat rectangular plate of known mass, width and breadth with a negligible thickness that lies in the horizontal xy-plane. The plate is suspended from a thin piece of piano wire that is in the vertical orientation coincident to the z-axis and where the piano wire is attached to the center of the plate. When the plate is subjected to a torque whose vector is coincident to the z-axis, the plate rotates in the horizontal plane such that the rotation of the plate is modelled as θ=Csin⁡(ωnt+ϕ). The parameter information is: mass of plate M = 1.2 kilogram width of plate W = 0.040 meter breadth of plate B = 0.075 meter shear modulus of piano wire G = 79.3 gigaPascals diameter of piano wire D = 0.003 meter length of piano wire L = 0.120 meter amplitude of rotation C = 0.087267520415 radian phase lag of rotation ϕ = 1.565872597159 radian Using the supplied information and any appropriate assumptions and / or approximations to determine the following; 1) the mass moment of inertia I 2)…

A space of mass 120 kg is going to use a planet for a gravitational assist- that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 280 m/s and at an angle of theta initial = 53 degrees, at a distance of 11500 km from the center of the planet. Given an expression for the angular momentum of the spacecraft using the coordinate system specified in terms of m, r0, v0, theta initial, and vector units i, j, k   If the spaceship whips around the planet to the other side so that the angle is theta 35 and is moving at 95 m/s, how far, in kilometers, from the planet is it?