Question

Determine experimentally which rotational axis yields the maximum rotational inertia (i.e., moment of inertia) and which yields the minimum rotational inertia for the broom stick. Draw a picture of the broom stick with its axis of rotation for (i) the minimum rotational inertia and (ii) the maximum rotational inertia.

Answer 1

the maximum is I₁ axis of rotation at the end

the minimum moment is I₂ axis of rotation at the center of mass

Step-by-step explanation:

For this exercise we use the definition moment of inertia

I = ∫ r² dm

for bodies of high symmetry it is tabulated; In this case we can approximate a broomstick to a thin rod, the moment of inertia with respect to a perpendicular axis when varying are

at one end

I₁ = ⅓ mL²

in in center

I₂ =
`(1)/(12)` m L²

There is another possible axis of rotation around the axis of the broom, in this case we have a solid cylinder

I₃ =
`(1)/(2)` m r²

remember that the diameter of the broom is much smaller than its length, therefore this moment of inertia is very small

when examining the different moments of inertia:

the maximum is I₁ axis of rotation at the end

the minimum moment is I₂ axis of rotation at the center of mass