5.4 Rotational Inertia

Rotational Inertia

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It plays a similar role in rotational motion as mass does in linear motion: just as mass resists changes in linear velocity, rotational inertia resists changes in angular velocity. Rotational inertia is a scalar, measured in units of kilograms meters squared (

{kgm^2}

), and represented with the variable

{I}

.

For a system with a single point particle rotating around an axis, its total rotational inertia can be represented with the equation below. This systems also works if there is a rod rotating about the end, which can just be seen as all of mass of the rod being at its center, and treating that as a point particle.

I=mr^2

{I}

represents the rotational inertia of the system of the point particle and the axis

${m}$ is the mass of the point particle
${r}$ is the distance of the point particle from the axis of rotation

If there are multiple point masses that are all being rotated, the total rotational inertia will just be a sum of their individual rotational inertias.

I_{tot}=\sum\limits_{i} m_ir_i^2

${I_{tot}}$ is the total rotational inertia of the system of the point particles and the axis - ${m_i}$ is the mass of each point particle
${r_i}$ is the distance of each point particle from the axis of rotation

For solid objects that are rotating, their rotational inertia will be the sum of each small mass and how far each mass is from the axis of rotation. With this obviously being very hard to do and requiring calculus, physicists have created formulas to find the rotational inertia of some simple solid objects when they are rotating about their center of mass. These formulas will be given on the AP Physics 1 Exam and do not need to be memorized.

MCQ Reading Checkpoint

Which object has the lowest rotational inertia, assuming each object has the same radius and the same mass?

Choose the best option:

Rotational Inertia

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