A molecule consists of identical atoms of mass m placed at each vertex of a regular hexagon of side a. Calculate the moment of inertia of the molecule about a. The z-axis that is perpendicular to the plane of the hexagon and passing through its center (6ma²) b. The y-axis that passes through two diametrically opposite atom (3ma²)

The moment of inertia of a uniform-density disk rotating about an axle through its center can be shown to be- . This result is obtained by using integral calculus to add up the contributions of all the atoms in the disk. The factor of 1/2 reflects the fact that some of the atoms are near the center and some are far from the center; the factor of 1/2 is an average of the square distances. A uniform- density disk whose mass is 18 kg and radius is 0.12 m makes one complete rotation every 0.4 s.

The oxygen molecule has a mass of 5.30 × 10' -26 kg and a moment of inertia of 1.94 × 10-46 kg m? about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

Consider an oxygen molecule (O2) rotating in the xy plane about the z axis. The axispasses through the center of the molecule, perpendicular to its length. The mass of each oxygen atom is 2.66 x 10-26 kg, and at room temperature the average separation between the two atoms is d=1.21 x 10-10 m (the atoms are treated as point masses). a) Calculate the moment of inertia of the molecule about the z axis. b) If the angular speed of the molecule about the z axis 4.60 x 1012 rad/s, what is its rotational kinetic energy?

Many molecules have a simple diatomic, dumbbell- like.Let us find the moments of iner tid about four exes. The bodies ore treated Os point particles with masses m, = 3.0 kg and m2= 5.0 Kg. Toke d, = 1.0 m and m2 = 2.0 m. %3D %3D В A C --G-o m1 d1 d2 m2 o-9--

9-2 In the linkage mechanism, as shown in Fig. P9-2, OA-CB AB=10 cm. 3 rad/s. Determine the angular velocity of AB and CB. when AOC-90° and 0.C. B are collincar. Fig. P9 -2

A star originates as a large body of slowly rotating gas. Because of gravitational attraction, this large body of gas slowly decreases in size. You can assume that no external forces are acting. Which one of the following statements correctly describes what happens as the radius of the body of gas decreases? O The angular momentum remains constant and the angular velocity increases. O The angular momentum increases and the angular velocity decreases. Both the moment of inertia and the angular velocity increase. Both the angular momentum and the angular velocity increase. Both the angular momentum and the angular velocity decrease.

What are the components of the moment of inertia of the BeBr2 body if the coordinates of the heritage sites and masses are in the following table atom X (A) y(A) z(A) mass 0 Be 0 0 9u Br 1.9 0 0 80u 0 -1.9 080u a-lc-la-la b-lolla c- lc> lo= la d-Is=la> la a Please answer within O b 60 minutes O C O d oc حيث ان u=1.67x1027 Kg

= Fn NVIDIA Consider five equal mass objects all with the same non-zero kinetic energy. Unless otherwise stated assume the axis of rotation is through the center-of-mass. Assume all densities are uniform or constant. 4 Order these objects from lowest angular velocity (1) to highest angular velocity (5). A V Type here to search FH alexa ENABLED V 7 Hoop of radius R (axis perpendicular to plane of disk). Solid disk of radius R (axis perpendicular to plane of disk). Solid sphere of radius R. Rod of length 2R (axis perpendicular to rod, axis through END of rod). Rod of length 2R (axis perpendicular to rod). Alt 4 A O 15 Et 1 ال 199+) O IA JU U Le 1 Raining now PE Ctrl = ASUS

A star originates as a large body of slowly rotating gas.Because of gravitational attraction, this large body of gas slowly decreases in size.You can assume that no external forces are acting.Which one of the following statements correctly describes what happens as the radius of the body of gas decreases? Both the moment of inertia and the angular velocity increase. Both the angular momentum and the angular velocity increase.     The angular momentum increases and the angular velocity decreases. Both the angular momentum and the angular velocity decrease. The angular momentum remains constant and the angular velocity increases.