In the figure below, m = 1.8 kg and M = 3.5 kg. Calculate the moment of inertia
ID: 1546820 • Letter: I
Question
In the figure below, m = 1.8 kg and M = 3.5 kg. Calculate the moment of inertia of the array of point objects shown in the figure about the vertical axis. Calculate the moment of inertia of the array of point objects shown in the figure about the horizontal axis. Assume the objects are wired together by very light rigid pieces of wire. the array is rectangular and it is split through the middle by the horizontal axis. About which axis would it be harder to accelerate this array? the horizontal axis neither axis the vertical axisExplanation / Answer
Given m = 1.8 kg, M = 3.5 kg
let from left mass m to M in the clock wise directon
m1 m2,M1,M2 are located at
about the vertical axis m1 is at (x1,y1) = (0.5m,0.25m)
0
m2 is at (x2,y2) = (1.5m,0.25m)
and M1 is at (X1,Y1) =(1.5m,0.25m)
M2 is at (X2,Y2) = (0.5m,0.25m)
mmoment of inertia about the vertical axis is
I = mR^2
Iv = m1r1^2+m2r2^2+M1R1^2_M2R2^2
Iv = 2((1.8+3.5)0.5^2)+2((3.5+1.8)*1.5^2) kg m2
Iv = 26.5 kgm2
about the horizontal axis is
Ih = m1r1^2+m2r2^2+M1R1^2_M2R2^2
Iv = 2((1.8+3.5)0.25^2)+2((3.5+1.8)*0.25 ^2) kg m2
Iv = 1.325 kg m2
T = I*alpha
as the moment of inertia is large the acceleration is less so
it is harder to accelerate about the vertical axis
answer is the vertical axis