The Uranian day is 17.24 hours. What is the speed of a point...

The Uranian day is 17.24 hours. What is the speed of a point on the equator of Uranus due to its rotation? Express your answer in $\mathrm{km} / \mathrm{hr}$. If the speed at the Earth's equator were the same, how long would our day be?

Key Concepts

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another to ensure consistency in calculations. In this problem, distances are measured in kilometers and time in hours, so it is important to perform appropriate conversions when calculating speed.

Linear Speed in Rotational Motion

Linear speed in rotational motion is calculated by dividing the distance traveled by the time it takes to travel that distance. For a planet, this means dividing the equatorial circumference by the rotation period, yielding the speed at which a point on the equator moves.

Proportional Reasoning

Proportional reasoning involves using ratios to compare relationships between different quantities. Here, it is applied by comparing the equatorial speeds and circumferences of Uranus and Earth to determine how the rotation period (length of a day) would change if a point on Earth moved at the same speed as one on Uranus.

Planetary Rotation

Planetary rotation refers to the spinning of a planet around its own axis. This rotation defines the length of a day on the planet and determines the linear speed of points on its surface, particularly along the equator where the circumference is greatest.

Circumference of a Circle

The circumference of a circle is the total distance around its edge and is calculated by the formula 2?r, where r is the radius. In the context of a planet, the equatorial circumference represents the distance a point on the equator travels during one full rotation.

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