Point particle A has a mass of 140 g and is located at (x, y, z) = (-1.0 cm, 5.5
ID: 1264031 • Letter: P
Question
Point particle A has a mass of 140 g and is located at (x, y, z) = (-1.0 cm, 5.5 cm, 0), point particle B has a mass of 275 g and is at (7.0 cm, 0, 0), and point particle C has a mass of 555 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
Rotational Inertia = mass * (distance from the axis of rotation)^2
RI = m * d^2
Particle A = 140 g at(-1, 5.5, 0)
Particle B = 275g at (7, 0, 0)
Particle C = 555 g at (-4.5, -3, 0)
a. X-Axis
Particle A is 5.5 above the x-axis, d = 5.5,
Particle B is on the x-axis, d = 0, so I = 0
Particle C is 3 cm below the x-axis, d = 3
? RIx = ? (m * d^2) = (140 * 5.5^2) + (555 * 3^2)
? RIx = ? 4235 + 4995 = 9230 g*cm^2
b. Y-Axis
Particle A is 1 cm to the left of the y-axis, d = 1
Particle B is 7 cm to the right of the y-axis, d = 7
Particle C is 4.5 cm to the left of the y-axis, d = 4.5
? RIy = ? (140 * 1^2) + (275 * 6^2) + (555 * 5^2)
? RIy = 140 + 9900 + 13875 = 23,915 g*cm^2
c. z-axis
To determine distance from z-axis, use Pythagorean Theorem
Particle A , d = (-1^2 + 5.5^2)^0.5 = ?31.25
Particle B, d = (7^2 + 0^2) ^0.5 = 7
Particle C, d = (-4.5^2 + -3^2) ^0.5 = ?29.25
? RIz = ? (140 * ?(31.25)^2) + (275 * 7^2) + (555 * ?(29.25)^2)
? RIz = 4375 + 13475 + 16233.75 = 34083.75 g*cm^2
d. What are the x and y-coordinates of the center of mass of the system?
Particle A = 140 g at(-1, 5.5, 0)
Particle B = 275g at (7, 0, 0)
Particle C = 555 g at (-4.5, -3, 0)
the origin is my reference point!
Center of mass = [(mass1 * distance from the origin) + (mass 2 * distance from the origin) + (mass 2 * distance from the origin)]