Question

Moment of inertia ofspoke not starting at rotational axis

Answer 1

Rotational inertia

Learn how the distribution of mass can affect the difficulty of causing angular acceleration.

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What is rotational inertia?

Rotational inertia is a property of any object which can be rotated. It is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis.

Rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics. Indeed, the rotational inertia of an object depends on its mass. It also depends on the distribution of that mass relative to the axis of rotation.

When a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system. Intuitively, this is because the mass is now carrying more momentum with it around the circle (due to the higher speed) and because the momentum vector is changing more quickly. Both of these effects depend on the distance from the axis.

Rotational inertia is given the symbol III. For a single body such as the tennis ball of mass mmm (shown in Figure 1), rotating at radius rrr from the axis of rotation the rotational inertia is

I = mr^2I=mr2I, equals, m, r, start superscript, 2, end superscript

and consequently rotational inertia has SI units of \mathrm{kg\cdot m^2}kg⋅m2.

Answer 2

Rotational inertia is important in almost all physics problems that involve mass in rotational motion. It is used to calculate angular momentum and allows us to explain (via conservation of angular momentum) how rotational motion changes when the distribution of mass changes.