Moments of inertia for some objects of uniform density:
disk I = (1/2)MR^2, cylinder I = (1/2)MR^2, sphere I = (2/5)MR^2
(a) A uniform disk has a moment of inertia that is (1/2)MR^2. A uniform disk of mass 16 kg, thickness 0.4 m, and radius 0.5 m is located at the origin, oriented with its axis along the y-axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y-axis and look toward the origin at the disk). The disk makes one complete rotation every 0.1 s.
What is the rotational angular momentum of the disk?
rot = kg·m^2/s
What is the rotational kinetic energy of the disk?
Krot = J
(b) A uniform sphere has a moment of inertia that is (2/5)MR^2. A sphere of uniform density, with mass 28 kg and radius 0.9 m, is located at the origin and rotates around an axis parallel to the x-axis. If you stand somewhere on the +x-axis and look toward the origin at the sphere, the sphere spins counterclockwise. One complete revolution takes 0.2 seconds.
What is the rotational angular momentum of the sphere?
rot = kg·m^2/s
What is the rotational kinetic energy of the sphere?
Krot = J
(c) A uniform rod has a moment of inertia for rotation around its long axis that is (1/2)MR^2. A cylindrical rod of uniform density is located with its center at the origin, and its axis along the z-axis. Its radius is 0.04 m, its length is 0.9 m, and its mass is 2 kg. It makes one revolution every 0.04 seconds. If you stand on the +z-axis and look toward the origin at the rod, the rod spins clockwise.
What is the rotational angular momentum of the rod?
rot = kg·m^2/s
What is the rotational kinetic energy of the rod?
Krot = J