Calculate the angular momentum for a rotating disk, sphere, and rod. (a) A unifo

Question

Calculate the angular momentum for a rotating disk, sphere, and rod. (a) A uniform disk of mass 18 kg, thickness 0.5 m, and radius 0.7 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 ty axis and look toward the origin at the disk). The disk makes one complete rotation every 0.7 s. What is the rotational angular momentum of the disk? What is the rotational kinetic energy of the disk? (Express your answer for rotational angular momentum in vector form.) Lrot = 4.41 X kg m2/s rot = (b) A sphere of uniform density, with mass 25 kg and radius 0.3 m, is located at the origin and rotates around an axis parallel with 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 0.6 s. What is the rotational angular momentum of the sphere? What is the rotational kinetic energy of the sphere? (Express your answer for rotational angular momentum in vector form.) kg m-/s rot rot = (c) A cylindrical rod of uniform density is located with its center at the origin, and its axis along the z axis. Its radius is 0.07 m, its length is 0.7 m, and its mass is 3 kg. It makes one revolution every 0.05 s. If you stand on the +x axis and look toward the origin at the rod, the rod spins clockwise. What is the rotational angular momentum of the rod? What is the rotational kinetic energy of the rod? (Express your answer for rotational angular momentum in vector form.) 2 kg m-/s rot rot -

Explanation / Answer

(A) I = M R^2 /2 = (18)(0.7^2) / 2

I = 4.41 kg m^2

w = 2pi / T = 2 pi / 0.7 = 8.976 rad/s

L = I w = 39.6 kg m^2/s along -ve y axis

L = - 39.6 j^ kg m^2/s

KE = I w^2 /2 = 178 J

(B) I = 2 M R^2 / 5 = 0.9 kg m^2

w = 2pi/0.6 = 10.47 rad/s

L = I w = 9.42 kg m^2/s

L = 9.42 i^

KE = I w^2 /2 = 49.3 J

(C) I = m L^2 / 12 = 3 x 0.7^2 / 12 = 0.1225 kg m^2

w = 2pi / 0.05 = 125.66 rad/s

L= I w i^2 (along x axis)

L = 15.4 i^

KE = I w^2 /2 = 967 J

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