Chapter 8, Problem 8.15P

If small particle 'm' is placed a distance 'x' from the central axis of a solid disk of total mass M with 'r' radius, what would the be force?

I don't understand why B would be the correct answer? Shouldn't the potential energy be decreasing as Mars gets farther, since the gravitational force decreases? And why is angular momentum the same?

Prove that the moment of inertia of a solid cylinder of uniform density, when rotating around its central axis,is MR2/2, where M is the mass of the cylinder and R is its radius. Hint: integrate the infinitesimal volume element in cylindrical coordinates

Consider the coordinate system in the diagram bellow; the z axis points out of the page. At the point (-d, 0, 0) a ball of mass m is initially  (at t= 0) at rest, but it is dropped under the face of gravity, near the Earth.  We ignore air resistance as usual, and treat ball as a point mass.  1.c) What is the angular momentum relative to the origin of the coordinate system?

Please explain. In the collision of disks, the system is not isolated because of existence of friction.How is it possible that conservation of angular momentum is still valid to a relativelygood accuracy?

Compute for the total moment of pt. A and pt. B Ps. with complete solution without any shortcuts, please

If a particle be describing an ellipse about a centre of force in the centre, show that the sum of the reciprocates of its angular velocities about foci is constant.

Consider the Atwood machine, where two masses m1 = 12.6 kg and m2 = 4.2 kg are connected by an ideal wire that passes through a pulley of mass M = E of radius R = 0.15 m. The pulley is attached, but can rotate freely around its axis of symmetry. As shown in the Figure below, at the initial instant the mass m1 is at a height h= 3.29 m in relation to m2. Knowing that the system starts from rest, and that the magnitude of the linear velocity of m1 when the masses pass through the same vertical position is v=3.31 m/s, what is the mass M of the pulley? Here, assume the acceleration due to gravity as g=10 m/s², the pulley moment of inertia as I=MR2 and, finally, that the wire does not slide on the pulley. Choose one: a. 4,2 kg b. 14,7 kg c. 10,5 kg d. 6,3 kg e. 12,6 kg f. 16,8 kg g. 8,4 kg h. None of the other alternatives.

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 300 km above the earth's surface; at the high point, or apogee, it is 4500 km above the earth's surface. What is the period of the spacecraft's orbit? Using conservation of angular momentum, find the ratio of the spacecraft's speed at perigee to its speed at apogee. Using conservation of energy, find the speed at perigee and the speed at apogee. It is necessary to have the spacecraft escape from the earth completely. If the spacecraft's rockets are fired at perigee, by how much would the speed have to be increased to achieve this? What if the rockets were fired at apogee?