13. Rotational Inertia & Energy

A uniform rectangular door of mass $M$ and width $w$ rotates about its hinges along one vertical edge. What is the moment of inertia of the door about the axis of rotation?

For a single particle of mass $m$ located at a distance $r$ from the axis of rotation, what is the moment of inertia $I$ of the particle?

For a particle labeled $a$ with mass $ma$ located at a distance $ra$ from the axis of rotation, what is its moment of inertia $Ia$?

Which of the following expressions gives the moment of inertia of a thin rectangular plate of width $b$ and height $h$ about the x-axis (along its base)?

For a thin rectangular plate of width $b$ and height $h$, determine the moment of inertia of the shaded area about the x-axis passing along its base.

A solid disc 4 m in diameter has a moment of inertia equal to 30 kg m² about an axis through the disc, perpendicular to its face. The disc spins at a constant 120 RPM. Calculate the mass of the disc.

Consider four point masses, each of mass $m$, placed at the corners of a square of side length $a$. What is the moment of inertia of the system about an axis that passes through the masses at corners $b$ and $d$ (i.e., along the diagonal of the square)?

Which of the following factors does the $\mathrm{moment} \mathrm{of} \mathrm{inertia}$ of an object depend on?

A system is made of two small masses (M_LEFT = 3 kg, M_RIGHT = 4 kg) attached to the ends of a 5 kg, 2-m long thin rod, as shown. Calculate the moment of inertia of the system if it spins about a perpendicular axis through the mass on the left.