## Now It's Your Turn: Self-Study Guide

###### ©1995 The Regents of the University of California

• Introduction
• Period of Rotation Examples
• Angular Velocity Examples
• Strategy

## Description:

Period of Rotation

The period of rotation of a Solar System object is the length of time it takes that object to spin once around on its axis. For example the Earth takes 24 hours to spin once around its axis. Its period of rotation is 24 hours or a day.

First, let's consider how to find the period of rotation of an object, be it a planet, orange, or basketball.

One way is to find a landmark or surface feature, and to measure the time it takes for an object to spin around and come back to the same spot. (Unfortunately, not all planets have a mark "stamped" on them. You'll have to find something to use as a landmark or surface feature later on.)

Before you start exploring with real planets, let's practice with something more simple, such as basketball.

Examples:

1. If a planet turns halfway (180 degrees) in 12 hours, how long will it take to go all the way around (360 degrees)?

Solution:

Known turn = 180 degrees
Full turn = 360 degrees
Known time = 12 hours
Full rotation time = ?
360 degrees / 180 degrees = Full rotation time / 12 hours
Full time rotation = 360 degrees/180 degrees x 12 hours = 24 hours

2. Often you can't see the planet during its entire rotation. (The Sun comes up in the morning and obscures our view of the planets; the planet slips behind clouds or below the horizon; etc.) Let's consider the following example.

We know that a surface feature of a rotating object covers 20 degrees in 4 hours. What is the period of its rotation? (To solve this problem, you will need to use some ratios.)

Solution:

Known turn = 20 degrees
Full turn = 360 degrees
Known time = 4 hours
Full rotation time = ?
20 degrees / 360 degrees = 4 hours / Full rotation time
Full time rotation = (360 degrees) (4 hours) / 20 degrees = 72 hours

3. Looks like you now understand what the period of rotation is, and are ready to work with rotation rates (or angular velocities, as they are sometimes called.)

## Angular Velocity

### We are approaching our GOAL - calculating the rotation rates (or angular velocity) of some planets.Remember, angular velocity is the angle by which an object turns in a certain time. Angular velocity can be expressed in degrees per unit time (second, minute, hour, etc.), radians per unit time, or even revolutions per unit time.

But first let's practice with some simple examples again. We will begin with racing cars.

Examples:

1. A circle has 360 degrees, right? So an Indycar driver speeds through 360 degrees every time she makes a lap (we'll use a circular race track). If the racer makes 360 degrees (one loop) in one minute, how many degrees per second does she cover?

Solution

To find the rotation rate, or angular velocity, you will need to divide the number of degrees by the number of seconds in one minute. The answer is: (360 degrees) / (60 seconds) = 6 degree/second

2. This problem is not about cars, it is about planets. Assume that a planetary feature moves 36 degrees in 4 hours. Use the angular velocity to find how long it takes for that feature to go all the way around the planet.

Solution

Known turn = 36 degrees
Known time = 4 hours
Full rotation time = ?
Angular velocity = 36 degrees / 4 hours = 9 degree/hour
Full time rotation = 360 degrees / 9 degree/hour = 40 hours

3. ## Strategy

You are ready now to figure out rotation rates (or angular velocities), and periods of rotation of some planets. But first, we want to give you some advice.

1. Pick a planet (go back to the Student Area Homepage and click one of the four buttons);

2. Look through all available images and data and choose two or three pictures (or a movie, like for the Saturn) to start with;

3. Pay attention to peculiar areas on the surface of the planets, and use them as landmarks or features;

4. Draw longitude lines on all your planetary pictures to make your work more efficient;

5. Prepare a transparent template for each planet, with longitude lines drawn every 20 degrees, for example (in this case you will have a portable angle measurer).

You are on your own now. You are pretty much equipped with all the necessary tools, you are well trained, and are ready for the adventure tour. Good luck!