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Engineering Mechanics II Practice Exam #3 1. Find the requested components of the inertia matrix for the compound slender bar shown. The bar has a linear density of 3 kg/m. (A slender bar has a moments of inertia about its short axes about its center of 1/12 M·L2, its moment of inertia about its long axis is zero, and its products of inertia about its center are zero). Ixx = ___________________ kg·m2 Iyy = ___________________ kg·m2 Iyz = ___________________ kg·m2 2. A certain rigid body has an inertia matrix with components given below, (also given in matrix form). What is the body’s moment of inertia if it is spun about an axis in the direction û , also given below? Ixx=20, Iyy=15, Izz=10, Ixy=0, Ixz=5, Iyz=5 (all in kilogram meters squared) 20 0 5 [I]= 0 15 5 kg·m2 5 5 10 3. 3 / 5 û 0 4 / 5 A certain rigid body has an inertia matrix with components given below, (also given in matrix form). What is the body’s angular momentum vector and its rotational kinetic energy if it is spun with angular velocity , also given below? Ixx=20, Iyy=15, Izz=10, Ixy=0, Ixz=5, Iyz=5 (all in kilogram meters squared) 20 0 5 [I]= 0 15 5 kg·m2 5 5 10 1 1 rad/sec 1 Hx = ___________________ kg·m2/s T = ___________________ J Hy = ___________________ kg·m2/s Hz = ___________________ kg·m2/s 4. A 8-kg spinning rod with extendable ends is rotating about an axis perpendicular to its 2 meter length at a rate of 20 rad/s. The arms then extend so that the rod becomes 3 meters in length. What is the new spin rate? MAE-2104 1 Ver. E, Rev 1 Engineering Mechanics II Practice Exam #3 5. A disk of mass 12 kg and radius R=0.5 m begins at rest. Forces A=100 N, B=200 N, and C=300 N (all perpendicular to the disk) act on the disk at time t=0. Find the acceleration of the center of mass of the disk and its angular acceleration at this instant. If the forces continue to act in the same direction relative to the disk, what is its angular velocity vector at t=2 s? [Moment of inertia through the center of mass and about the z axis is (1/2)*M*R2 and about the x or y axis is (1/4)*M*R2 ]. 6. At the instant shown, the tower crane is rotating about the z axis with an angular velocity 1 = 0.25 rad/s, which is increasing at 0.6 rad/s2. The boom OB is rotating downward with an angular velocity 1 =0.6 rad/s2 2 = 0.4 rad/s, which is decreasing at 0.8 rad/s2. B Determine the total angular velocity and angular acceleration of the boom Calculate the velocity and acceleration of point B located at the top of the boom. 2 =-0.8 rad/s2 7. At the instant shown, the base of the robotic arm is turning about the z axis with an angular velocity of 1 =4 rad/s, 1 = 3 rad/s2. Also, the boom segment BC is rotating at BC = 8 rad/s, which is increasing at BC = 2 rad/s2. The gripper is retracting at a constant rate which is increasing at vC=1 m/s vC =1 m/s relative to the arm. Calculate the inertial velocity of point C. (extra) Find the acceleration of point C. MAE-2104 2 Ver. E, Rev 1