2 The Rotational Inertia of a Disk The basic equation for the moment of inertia

Question

2 The Rotational Inertia of a Disk The basic equation for the moment of inertia of a point mass isNote that as r increases I increases, rather dramatically, as the square of r. Let's consider the rolling motion of a hoop and disk both having the same mass and radius. To make the observation of rotational motion your class will need one setup of the following demonstration apparatus: . 1 hoop . 1 disk . 1 ramp Recommended group size All Interactive demo OK?: 12.11.2. Activity: Which Rotational Inertia Is Larger? a. If a hoop and a disk both have the same outer radius and mass, which one will have the larger rotational inertia? Hint: Which object has its mass distributed farther away from an axis of rotation through its center? Why? b. Which object should be more resistant to rotation-the hoop or the disk? Explain. Hint: You may want to use the results of your obser- vation in Activity 12.9.1c. Disk c. What will happen if a hoop and disk each having the same mass and outer radius are rolled down an incline? Which will roll faster? Why? Fig. 12.15. A disk rolling down an incline. d. What did you actually observe, and how valid was your prediction? Hoop Fig. 12.16. A hoop rolling down an incline

Explanation / Answer

a)

The hoop has a higher moment of inertia. It is because it's mass is distributed more around the edges (a higher radius) than closer (a smaller radius).

b)

More the inertia, more is the resistance. So the hoop is more resistant to rotation.

c)

Disk will roll faster. More the rotational inertia, less is the rotatational speed. So, the disk having less inertia has more speed.

d)

You will observe that the disk reaches the bottom before the hoop. This proves that the disk was rolling faster.

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