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# Rotational Inertia: Resistance to Change in Rotary Motion

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Author: Janice VanCleave

Inertia refers to the tendency of an object to remain at rest or to resist any change in its state of motion unless acted on by an outside force. All objects, whether stationary or in motion, have inertia. Rotational inertia is the property of an object that resists any change in rotary motion, which is motion about the axis of an object.

In this project, you will measure the torque (turning effect) required to overcome an object's rotational inertia. You will determine the effect of the radius of an object on its rotational inertia. You will also determine the effect of the location of the center of mass on rotational inertia.

### Getting Started

Purpose: To measure the torque required to overcome an object's rotational inertia.

### Materials

• 1 roll of new adding machine tape
• -by-36-inch (0.94-by-90-cm) dowel
• golf ball-size piece of modeling clay
• 20 to 25 small paper clips

### Procedure

1. Place the roll of adding machine tape on the dowel. This will be roll A.
2. Divide the clay in half and use the two pieces to support the dowel on the backs of two chairs.
3. Clip one paper clip on the end of the paper strip. Straighten a second paper clip to form a hook, and attach it to the first paper clip on the paper strip, as shown in Figure 10.1.
4. Add one paper clip at a time to the hook until the paper starts to unroll. Record the number of paper clips required to make the roll begin to turn as the torque in a Rotational Inertia Data table like Table 10.1.

### Results

The number of paper clips will vary depending on different factors, including the size and weight of the paper roll. The roll used by the author required 18 paper clips.

### Why?

Rotational inertia is the property of an object that resists any change in rotational motion (turning about an axis). If the rotational inertia of a stationary object is great, it takes a greater amount of torque to spin the object. Torque is the turning effort applied to an object that tends to make the object rotate. Torque is the product of a force and its perpendicular distance from a point about which it causes rotation to the axis of rotation. Just as a force applied to an object tends to change its translational motion, so a torque applied to an object tends to change the object's rotational motion. Since each paper clip applies a force on the paper roll at a perpendicular distance equal to the radius of the roll, each paper clip added increases the torque on the roll. The amount of torque needed to turn the paper roll indicates the magnitude of the roll's rotational inertia. Thus the more torque, indicated by the number of paper clips required to turn the roll, the greater is the rotational inertia of the roll.

### Try New Approaches

How does the radius of an object affect its rotational inertia? Repeat the investigation using a second roll of tape with half the radius of the original one used. Add your findings to the Rotational Inertia Data table for this roll; called roll B. Note the radii of the two rolls.

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