Calculate the moments of inertia I1, I2, and I3, for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the x3-axis along the axis of symmetry of the cone. Choose the origin at the apex of the cone, and calculate the elements of the inertia tensor. Then make a transformation such that the center of mass of the cone becomes the origin, and find the principal moments of inertia.
Answer to relevant QuestionsCalculate the moments of inertia I1, I2, and I3, for a homogeneous ellipsoid of mass M with axes’ lengths 2a > 2b > 2c.A door is construct of a thin homogenous slab of material: it has a width of 1m. If the door is opened through 90o, it is found that on release it closes itself in 2s. Assume that the hinges are frictionless, and show that ...If a physical pendulum has the same period of oscillation when pivoted about either of two points of unequal distances from the center of mass, show that the length of the simple pendulum with the same period is equal to the ...Show by the method used in the previous problem that the determinant of the elements of a tensor is an invariant quantity under a similarity transformation. Verify this result also for the case of the cube.Solve Example 11.2 for the case when the physical pendulum does not undergo small oscillations. The pendulum is released from rest at 67o at time t = 0. Find the angular velocity when the pendulum angle is at 1o. The mass of ...
Post your question