Point particle A has a mass of 115 g and is located at (x, y, z) = (-1.0 cm, 4.5
ID: 1446370 • Letter: P
Question
Point particle A has a mass of 115 g and is located at (x, y, z) = (-1.0 cm, 4.5 cm, 0), point particle B has a mass of 275 g and is at (6.5 cm, 0, 0), and point particle C has a mass of 470 g and is at (-4.5 cm, -3.0 cm, 0). Find the rotational inertia of the system of point particles shown in the figure assuming the system rotates about the following axes. (a) x-axis g cm2 (b) y-axis g cm2 (c) z-axis (The z-axis is perpendicular to the xy-plane and points out of the page.) g cm2 (d) What are the x and y-coordinates of the center of mass of the system? xCM = cm yCM = cm
Explanation / Answer
A) Ix = (115*4.5^2)+(275*0^2)+(470*3^2) = 6558.75 gm cm^2
B) Iy = (115*1^2)+(275*6.5^2)+(470*4.5^2) = 21251.25 gm.cm^2
C) Iz = (115*(1^2+4.5^2))+(275*6.5^2)+(470*(4.5^2+3^2)) = 27810 gm.cm^2
d) Xcm = ((-115*1)+(275*6.5)-(470*4.5))/(115+275+470) = -0.514 cm
Ycm = ((115*4.5)+(275*0)-(470*3))/(115+275+470)
Ycm = -1.03 cm