Consider a stick 1.00 m long and its moments of inertia about axes perpendicular to the stick's length and passing through two different points on the stick: first, a point at its center and second, a point 17 cm from one end. Calculate the ratio I2/11, the ratio of the second moment of inertia to the first. 12 I₁ || Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary.

Ixx Izy Izz --(29 Iyx Iyy lyz Iza Izy Izz, I = For a set of discrete mass m, with cartesian coordinates (xi, yi, Zi) connected by massless rod, the components of the moment of inertia can be obtained using the following elations: Ixx = Σmi(y² + z²) Iyy = Σm₂(x² +2²) Ixy I = i Izz = [m₂(x² + y²) i = Iyx = -mixiyi Izz = Izx = - Iyz = Izy 4ma² 0 0 -Σmix izi -Σmiyizi == 0 4ma² 0 0 0 8ma² (b) A rigid body consists of three point masses of 2 kg, 1 kg, and 4 kg connected by massless rod. These masses are located at coordinates (1, -1, 1), (2,0, 2), and (-1, 1,0) (in meters) respectively. Using the formulae given for the components of the moment of inertia tensor, compute the inertia tensor of this system. What is the angular momentum vector of this body if it is rotating with an angular velocity w=(3, -2, 4)? • Find the principal moments and a set of principal axes.

Solid cylinder about axis R A solid cylinder has a mass 2.45kg and a radius 0.746 m. What is its moment of inertia (in unit of kgm2) when it is rotating around its own central axis? (please search your physics text book or other sources for the correct formula for this situation, you lab manual does not necessarily have the formula.)

Computation. A uniform solid sphere has mass M = 8.9 kg and radius R = 0.2 m. What is its moment of inertia about an axis tangent to its surface? I- 2 kg .m² Record your your numerical answer below, assuming three significant figures. Remember to include a as necessary.

During a steady right turn, a person exerts the forces shown on the steering wheel. Note that each force consists of a tangential component and a radially-inward component. Determine the moment exerted about the steering column at O. The moment will be positive if counterclockwise, negative if clockwise. 9.4 N 28 17° 17⁰ Answer: M = 430 mm i 28° 9.4 N B N-m

Using I = xM/L dx, prove that the moment of inertia about the y'-axis at the end of the rigid rod in the figure is (1/3)ML. (Submit a file with a maximum size of 1 MB.) dx L. 2