(a) A uniform, thin rod of length L and mass M has a frictionless pivot at one end. Starting from the definition of moment of inertia as I = | r² dm, show that the rod has a moment of inertia given by 1 -ML². 3 (b) The rod is initially vertical (with the pivot at the bottom) and falls under gravity. By considering that gravity acts on the rod's center of mass, find the torque acting on the rod when it is at an angle 0 to the vertical, and hence show that the angular acceleration

As a physics demonstration, a special bowling ball is made so that it can be rotated about its center of mass to get a feel for how "big" a moment of inertia of 1 kg⋅m2 is. The average bowling ball has a weight of 15.4 lbs and a circumference of 26.3 inbut it does not have a moment of inertia equal to 1 kg⋅m2.Since the sporting goods manufacturer has no understanding of how "big" 1 kg⋅m21  is, calculate the diameter ? demo of the demo bowling ball, in inches, that it will need to manufacture. Assume that bowling balls are solid, with a constant density.   D of demo required in inches.

Consider a homogeneous rigid body with a non-uniform distribution of mass. The body is rotating about a fixed axis. Which of the following statements about the moments of inertia is correct? A) The principal axes of inertia will coincide with the axis of rotation. B) The moment of inertia about the axis of rotation will be the smallest possible. C) The moment of inertia about any axis parallel to the axis of rotation will be constant. D) The moment of inertia tensor will be diagonal, with all diagonal elements distinct. Choose the correct option and justify your choice.

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ʼn = 0.315 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0588 m thick, made out of a material with a density of 7370 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? ℗ la ro rd = m

A 7.33 kg particle with velocity (1.80 m/s)i (6.97 m/s ) is at x = 5.08 m, y = 3.64 m. It is pulled by a 5.87 N force in the negative x direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing? (a) Number i (b) Number (c) Number I i = k Units k Units k Units >