Find the maximum and minimum moments of inertia with respect to axes through point 0 of the shaded area shown in the figure below.
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- A 5 kip force acts on point A of rod AB as shown. Rod AB is 15 in long. The angle α = 8°. Determine the magnitude in kips and direction in degrees counterclockwise from the +x-axis of the smallest force that will create the same moment about point B as does the 5 kip force. Magnitude - __________(kips) Direction - __________(degrees counterclockwise from the +x axis)Moment of inertia Derive the formula for the moment of inertia of a uniform thin rod of length L and mass M about an axis through its center, perpendicular to its face. Repeat the calculation, only now assume the rod has a density that increases uniformly from a value of po on one end to 2po on the other end. Suggestion For the second integration, it is important to define the density function correctly: It will be a straight line that includes the two points (-L/2, po) and (L/2, 2po). Find the slope of the line as rise of run, and the x-intercept, p(0). Total mass of the rod, M, will be the integral of the density function from -L/2 to L/2. If you solve the second integration correctly, including the value of the total mass, M, in terms of p, you should see a very interesting relationship between the two moments of inertia.Show complete solution and the fbd
- Yo-Yo man releases a yo-yo from rest and allows it to drop, as he keeps the topend of the string stationary. The mass of the yo-yo is 0.059 kg, its moment of inertia is2.5 * 10–5 kg · m2, and the radius r of the axle the string wraps around is 0.0068 m. Whatis the linear speed v of the yo-yo after it has dropped through a height of h = 0.50 m?Determine the moment of inertia of a solid homogeneous cylinder of radius R and length L with respect to a diameter in the base of the cylinder.The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia l?
- Find the moment of inertia for a uniform rod (mass m and length L) about an axis at the position shown in the figureFind the moment of inertia for a solid cube is bounded by planes x = F1, z = 71 , y = 3 and y = 5 about x – axis(a) Determine the centroidal polar moment of inertia of a circular area by direct integration. (b) Using the result of part (a), determine the moment of inertia of a circular area with respect to a diameter.