Rotational inertia

Why is a Ferris wheel slow to start up or stop? An object’s rotational inertia is its resistance to changing its state of rotation—increasing or decreasing its angular velocity. A wheel with low rotational inertia is easy to spin. An amusement-park Ferris wheel starts and stops very slowly because the heavy steel structure has a large rotational inertia. Racing cars and bicycles have very light aluminum-alloy wheels to reduce rotational inertia. Read the text aloud
Which has a greater rotational inertia?Rotational inertia depends not only on mass and rotational speed but also on how mass is distributed around the axis of rotation. Consider a solid cylinder and a hoop with the same mass m rotating at the same angular velocity ω. Now think about a small element of mass inside each object. Mass element (B) is moving faster than mass element (A) because point (B) is farther from the axis of rotation than point (A). A hoop has more rotational inertia than a cylinder of equal mass at the same angular velocity because the mass in the hoop is moving faster because of its greater distance from the axis of rotation. Read the text aloud
The quantity of rotational inertia possessed by an object called its moment of inertia and is identified with a capital letter “I” in equation (13.1). The units of I are kg m2. Notice that the moment of inertia varies with the square of the radius. That means that mass that is twice as far from the center of rotation contributes four times as much rotational inertia. Read the text aloud
(13.1) I=m r 2
I  = moment of inertia (kg m2)
m  = mass (kg)
r  = radius (m)
Moment of inertia
of a point mass
How is the moment of inertia different for these two situations?
To get a sense of how mass distribution changes rotational inertia, consider a light wooden pole with two 1 kg iron masses. When the masses are 0.1 m from the center, the moment of inertia is 0.02 kg m2. When the masses are 1.0 m from the center, the moment of inertia is a hundred times larger, even though the total mass is identical! Consequently, it takes a hundred times more torque to change the rotational speed when the masses are spread out. Read the text aloud Show Walking a tightrope
A professional cyclist is designing his ideal bicycle for racing. Should he make the rims of his wheels heavy or light? Use the rotational properties of the wheel in your answer. Show

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