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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 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 4. 1 1 rad/sec 1 A certain rigid body has an inertia matrix with components given below, (also given in matrix form). What is the body’s 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 MAE-2104 1 1 rad/sec 1 1 Ver. B, Rev 1 Engineering Mechanics II Practice Exam #3 5. A square plate of mass 12 kg and side length a=0.5 m has an angular velocity 1 = 8 rad/s while rotating on a smooth surface. Determine its new angular velocity just after its corner strikes and hooks onto the peg and the plate starts to rotate about P without rebounding. (Moment of inertia about the vertical axis through the middle of the plate is (1/12)*m*(a2 + a2) ) 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 2 = 0.4 rad/s, which is increasing at 0.8 rad/s2. 1 =0.6 rad/s2 B Determine the total angular velocity and angular acceleration of the boom Calculate the velocity 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. Calculate the velocity of point C. (extra) Find the acceleration of point C. MAE-2104 2 Ver. B, Rev 1