what is the directions of the moments produced by force F about points B, C, and D, respectively?
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what is the directions of the moments produced by force F about points B, C, and D, respectively?
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- Write down the inertia tensor for a square plate of side ? and mass ? for a coordinate system with origin at the center of the plate, the z-axis being normal to the plate, and the x- and y- axes parallel to the edges.Hamiltonian of a system is given by: Sum of momentum and speed Sum of KE and PE Difference between KE and PE The square root of momentum + speedA stick of length L and mass M1 is in free space (no gravity) and not rotating. A point mass m2 hasinitial velocity v heading in a trajectory perpendicular to the stick. The mass has a perfectly inelasticallycollision a distance b from the center of the stick. Find the velocity of the center of mass and the finalangular velocity.
- A particle of mass m is located at x = 1, y = 0,2 = 2. Find the tensor of inertia for the particle relative to the origin. The particle rotates about the z axis through a small angle a <<1 as shown below. Show that the moments of inertia are unchanged to second order in a but the products of inertia can change linearly with a.(a) What does the quadrupole formula (P) = = = (Qij Q³ ³) compute? Reason the answer. (b) A point mass m undergoes a harmonic motion along the z-axis with frequency w and amplitude L, x(t) = y(t) = 0, z(t) = L cos(wt). Show that the only non-vanishing component of the quadrupole moment tensor is = Im L² cos² (wt). (c) Use the quadrupole formula to compute the power radiated by the emission of gravitational waves. (Hint: recall that (cos(t)) = (sin(t)) = 0 and (cos² (t)) = (sin² (t)) = ½½ for a given frequency 2.)