Please help I tried solving this but I cant seem to get it right. Five objects o
ID: 1375220 • Letter: P
Question
Please help I tried solving this but I cant seem to get it right.
Five objects of equal mass are shown below together with the axis about which they are rotating. Select the objects in order of increasing rotational energy. If B has the smallest rotational energy, then A, C, D, and finally E with the largest rotational energy, enter BACDE (Note: If multiple objects have the same rotational energy, then enter them in the order they appear below.)The physical parameters of the various objects are on the printed assignment.
**this question was closed because it wasnt "one" question, but this IS one question on my homework!
Five objects of equal mass are shown below together with the axis about which they are rotating. Select the objects in order of increasing rotational energy. If B has the smallest rotational energy, then A, C, D, and finally E with the largest rotational energy, enter BACDE (Note: If multiple objects have the same rotational energy, then enter them in the order they appear below.)The physical parameters of the various objects are on the printed assignment. Thin cylindrical shell, about cylinder axis with R = 2m and w = 6rad/s(Note: Moment of inertia of a thin cylindrical shell is the same as that of a thin hoop, just M R^2) Thin rod, about axis through center, perpendicular to the length with l = 8m and w = 5rad/s Solid Cylinder, about cylinder axis with R = 3m and w = 5rad/s Solid Sphere, about any diameter, with R = 4m and w =5rad/s Thin Spherical shell, about any diameter, with R = 2m and w=7rad/s (Note: Moment of inertia of such a thin shell is (2/3) M R^2)Explanation / Answer
A)
Moment of inertia of shell, I = MR^2
So, Its rotational energy, K.E,rot = 0.5*I*W^2 = 0.5*(MR^2)*W^2
K.E,rot = 0.5*M*(WR)^2 = 0.5*M*(6*2)^2 = 72*M
B)
I = ML^2/12
K.E,rot = 0.5*(ML^2/12)*W^2
= M*(WL)^2/24
= M*(5*8)^2/24
= 66.7*M
C)
I = 0.5*MR^2
K.E,rot = 0.5*(0.5*MR^2)*W^2
= 0.25*M*(WR)^2
= 0.25*M*(5*3)^2
= 56.3*M
D)
I = (2/5)*MR^2
So, K.E,rot = 0.5*(2/5)*(MR^2)*W^2
= (1/5)*M*(WR)^2
= 80*M
E)
I = (2/3)*MR^2
So, K.E,rot = 0.5(2/3)*MR^2*W^2
So, K.E,rot = (1/3)*M*(WR)^2
= 65.3*M
So, answer is : C < E < B < A < D