# Moment of inertia of a system of masses

## Homework Statement

The moment of inertia about an axis through the center of mass of a system consisting of two masses 3.0 and 5.0 kg connected by a rod of negligible mass 0.8m long is

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I = I1 + I2

## The Attempt at a Solution

I added all the moments of inertia of the system about the middle (0.4m)

I = m1R^2 + m2R^2 = (m1 + m2) * R^2 = (3 + 5) * 0.4^2 = 1.28

However, 1.28 is not the right answers. Does anyone know where I went wrong?

I am no expert but my syllabus is same
I am trying for practice
(m1+m2)R=m1r1+m2r2
8(R)=3(0)+5(0.8)
8R=4
R=1/2
Mment of inertia=MR^2
=8 1/4
=2 Kg m^2
is this correct plz tell me

I am no expert but my syllabus is same
I am trying for practice
(m1+m2)R=m1r1+m2r2
8(R)=3(0)+5(0.8)
8R=4
R=1/2
Mment of inertia=MR^2
=8 1/4
=2 Kg m^2
is this correct plz tell me
Could you explain what this equation means:

(m1+m2)R=m1r1+m2r2

haruspex
Homework Helper
Gold Member
2020 Award
the center of mass of a system

moments of inertia of the system about the middle (0.4m)
Is that the centre of mass?

Could you explain what this equation means:

(m1+m2)R=m1r1+m2r2
Learn this equation which i have given
(m1+m2)R=m1r1+m2r2
where m1 and m2 are the given masses
r1 and r2 are their respective positions
R is the position of center of mass

The first move is to establish the location of the center of mass. It is the balance point where the torques due to the different weights are equal and opposite. Then the moment of inertia can be calculated as the sum of the m r^2 terms.

kuruman
Homework Helper
Gold Member
The first move is to establish the location of the center of mass. It is the balance point where the torques due to the different weights are equal and opposite.
Are torques and weights needed to find the center of mass of this and other systems?

Another way to find the center of mass is to suspend the body and a plumb bob from the same suspension point and repeat using a different point of suspension. Where the two plumb lines cross is the location of the c.m.

kuruman
Homework Helper
Gold Member
Another way to find the center of mass is to suspend the body and a plumb bob from the same suspension point and repeat using a different point of suspension. Where the two plumb lines cross is the location of the c.m.
Isn't there a mathematical way to find the CM using algebra?

Certainly. If you Google center of mass you will find several equations.

kuruman