Question

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows thatA dumbbell-shaped object is composed by two equal masses, , connected by a rod of negligible mass and length . If is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and is the moment of inertia with respect to an axis passing through one of the masses, it follows thatI1 = I2.I2 > I1.I1 > I2.

Answer 1

I2> I1. True. I2 is double I1

Step-by-step explanation:

To answer this exercise let's calculate the moment of inertia of each configuration, approach the bodies to specific masses, so the moment is

I = m r²

The axis passes through the center of the bar of length r

I1 = m (r / 2)² + m (r / 2)²

I1 = m r² (¼ + ¼)

I1 = ½ m r²

The axis passes through one of the masses

I2 = m r² + 0

We compare the two are the values

I1 = ½ I2

I2 = 2 I1

Let's review the values ​​the statements of the exercise

I1 = I2. False. The moments are different.

I2> I1. True. I2 is double I1

I1> I2. False. It's the opposite