Two spheres have the same diameter and mass, but one is solid and the other one...

Two spheres have the same diameter and mass, but one is solid and the other one is hollow. Assuming homogeneous densities and putting the origin at the center, calculate the inertia tensor of each sphere.

Expert Solution

For the solid sphere, note that the off diagonal terms are 0. Because:

And since the sphere is symmetric, the result holds. For the diagonal terms, we do the following:

Thus the tensor reads:

For the hollow sphere, the same argument as above gives us that the off diagonal terms are all 0. For the diagonal terms, we assume that the shell has a small thickness . Then:

Thus the tensor reads:

genius_generous answered 1 year ago

Two spheres, one solid, one a thin shell, each have a mass of 0.89 kg and...

Two spheres, one solid, one a thin shell, each have a mass of 0.89 kg and a radius of 11 cm. They are given the same torque of 0.13 mN acting for 7 s. Which sphere is rotating faster?

To solid spheres (perfectly-conducting) have a volumetric mass density ρ. One of the spheres has a...

To solid spheres (perfectly-conducting) have a volumetric mass density ρ. One of the spheres has a radius of R (has a net charge -Q) and the other has a radius of 2R (with a net charge of 2Q). They are released from rest with their centers 6R apart in a vacuum in no gravitational field. Part 1: At what speeds are the spheres moving when they strike each other? Part 2: If they rebound elastically and can transfer charge by...

Two cars are on a level air track. They have the same mass as each other....

Two cars are on a level air track. They have the same mass as each other. The red car is given a push so that it moves toward the blue car with an initial speed of 2 m/s, while the blue car is given a push so that it moves toward the red car with an initial speed of 4 m/s. If the cars completely stick together, find their combined speed after the collision. 2. This is an inelastic collision,...

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius....

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius. They both roll without slipping, have the same linear speed and approach the same inclined plane. As they roll up the inclined plane, they continue to roll without slipping. Which object will reach the greatest height on the inclined plane? A: solid homogeneous cylinder B: solid homogeneous sphere C: they both reach the same maximum height If you could explain why in your answer...

Two solid metal spheres of different radii are far apart. The spheres are connected by a fine metal wire. Some charge is placed on one of the spheres.

Two solid metal spheres of different radii are far apart. The spheres are connected by a fine metal wire. Some charge is placed on one of the spheres. After electrostatic equilibrium is reached, the wire is removed. Which of these quantities will be the same for the two spheres?(a) The charge on each sphere(b) The electric field inside each sphere, at the same distance from the center of the spheres(c) The electric field just outside the surface of each sphere(d)...

Two objects, one having three times the mass of the other, are dropped from the same...

Two objects, one having three times the mass of the other, are dropped from the same height in a vacuum. At the end of their fall, their speeds are the same because: Select one: a. all objects reach the same terminal velocity b. the force of gravity is the same for both objects c. the acceleration of the largest object is three times greater than that of the smallest object d. no option displayed e. everything that falls into the...

Two solid spheres are running down from incline of height 3.7 m. Sphere A has mass...

Two solid spheres are running down from incline of height 3.7 m. Sphere A has mass 3.3 kg; radius 15.7 cm; sphere B has mass 7.4 kg and radius of 39.3 cm. Find the ratio of their angular velocities omegaA/omegaB at the bottom of the incline.

Two 2.0-cm-diameter insulating spheres have a 5.60 cm space between them. One sphere is charged to...

Two 2.0-cm-diameter insulating spheres have a 5.60 cm space between them. One sphere is charged to + 40.0 nC , the other to - 60.0 nC . Part A What is the electric field strength at the midpoint between the two spheres?

Two 2.0-cm-diameter insulating spheres have a 7.00 cm space between them. One sphere is charged to...

Two 2.0-cm-diameter insulating spheres have a 7.00 cm space between them. One sphere is charged to + 70.0 nC , the other to - 79.0 nC . Part A What is the electric field strength at the midpoint between the two spheres? Express your answer with the appropriate units.

Two titanium spheres approach each other head-on with the same speed and collide elastically. After the...

Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 200 g, remains at rest. (a) What is the mass of the other sphere? (b) Assume that the initial speed of each sphere was 2.2 m/s. What is the speed of the two-sphere center of mass?

Question