b. Let p dv be the mass of an element of a solid of volume V, where p is the mass of unit volume. Then the moment of inertia of the solid of volume V about the x-axis is given by, M.1.x-axis = p(y² +2²) dv V Find the moment of inertia of the uniform solid in the form of octant of the ellipsoid x² + y² + z² = 4; for z> 0 about the x- axis.
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- going to calculate the theoretical value of the moment of inertia of the rotor, using the measurements given below. The rotor consists of 4 cylindrical segments which are fused together. The moment of inertia of a solid cylinder is I = (1/2)MR^2. To calculate I for the rotor, add the individual I values of the 4 cylindrical segments. This means that you will have to calculate the mass of each segment. Assume that the density of the rotor (M/V) is uniform. Recall that the volume of a cylinder is given by V = πR^2L.Problem 4: A 20-N horizontal force is applied perpendicular to the handle of the socket wrench. Determine the magnitude and the coordinate direction angles of the moment created by this force about point O. What is the moment about the z-axis? 75 mm 200 mm 20 N 15°Joe's shoulder is labeled S and two points on the cable are labeled P and B. The coordinates of the three points are given below and the tension in the cable is 200 N. Find the moment about Joe's shoulder. Point S P B X (m) 0.68 0 1.9 Y (m) 0.9 3.2 1.1 z (m) 1.4 0 1.4
- 9. The figure at right depicts the following situation: a thin uniform rod of length L = 3.0 m and mass M = 4.0 kg is free to pivot about a frictionless axle parallel to the z-axis and passing through its midpoint. The moment of inertia of the rod about the axle is =MI². Initially the rod is at rest, hanging vertically. A small clay ball of mass m = 1.0 kg is shot at the rod with velocity = (1.0"), and it impacts the rod at a distance L/3 below the pivot point. The clay ball sticks to the rod, and they both swing together in an upward arc. If the putty ball swings to a final maximum height h above the point where it first struck the rod, what is the height h? A) 0.003 m B) 0.013 m C) 0.027 m D) 0.043 m E) 0.067 mA circular cone with constant density 1, base radius 6, and height 8 is placed so the axis of symmetry is on the z-axis. A cylindrical hole of radius 1 is drilled through the axis of symmetry. Find the moment of inertia of the remaining shape. (The moment of inertia about the z-axis will be the same no matter where the shape is placed along the z- axis and whether the shape is pointing up or pointing down.)Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rb=2R are connected by a thin, uniform rod of length L=2R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical factor in fraction form.
- A square with length 20 cm on each side is subjected to forces as shown in the figure. Find the net torque around point O. Given mg = 10 N T1 (normal to the diagonal line ) = 10 N T2 = 5 N. T3 = 20 N at half way to the top of the square. theta1 = 30 degree. In this problem specify your direction using (+) for ccw, and (-) for cw directions around O.You have been given the following solid cone. The cone has a mass (m), height (h) and a base with a radius (r). Prove that the moment of inertia of the cone about its central axis is equal to (3/10)mr² (independent of h). N hModern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared. b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities. c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.
- A kitchen door is attached to a vertical support by a set of hinges. Assume the door is uniform and has height 2.40 m, width 0.865 m, and mass 21.0 kg. A. Determine its moment of inertia (in kg · m2) for rotation on its hinges. B. Are any pieces of data unnecessary? (Select all that apply.) The height of the door is unnecessary. The width of the door is unnecessary. The mass of the door is unnecessary. No; all of the data are necessary.The uniform square steel plate has a mass of 7 kg and is resting on a smooth horizontal surface in the x-y plane. If a horizontal force P = 101 N is applied to one corner in the direction shown, determine the magnitude of the initial acceleration of corner A. The distance b = 235 mm. Part 1 b P 50° b What is the mass moment of inertia about a z-axis through the center of mass? Answer: IG i eTextbook and Media kg m2The member shown below is fixed at O and its dimensions are h1h1 = 1.10 mm, h2h2 = 0.20 mm, and ww = 0.50 mm. A force F of magnitude F=160N is applied at point C. Determine the magnitude of the moment of the force about point O.