Calculating Planet Equator Point Speed

The question asks us to find the speed of a point on the equator of a planet given its circumference and the time it takes for one complete rotation. This speed is essentially the distance covered by a point on the equator in one rotation divided by the time taken for that rotation.

Here's the information provided:

• Circumference of the planet = 36,000 km
• Time for one complete rotation (Period) = 20 hours

We need to find the speed in meters per second (m/s).

Step-by-Step Calculation of Equatorial Speed

First, we need to convert the given measurements into the required units (meters and seconds).

1. Convert Circumference from kilometers to meters:

1 kilometer = 1000 meters

Circumference = \(36,000 \text{ km} = 36,000 \times 1000 \text{ m} = 36,000,000 \text{ m}\)

2. Convert Rotation Period from hours to seconds:

1 hour = 60 minutes

1 minute = 60 seconds

1 hour = \(60 \times 60\) seconds = 3600 seconds

Rotation Period = \(20 \text{ hours} = 20 \times 3600 \text{ seconds} = 72,000 \text{ seconds}\)

3. Calculate the speed:

The speed of a point moving in a circle is given by the formula:

Speed = \(\frac{\text{Distance}}{\text{Time}}\)

In this case, the distance is the circumference of the planet, and the time is the rotation period.

Speed = \(\frac{\text{Circumference}}{\text{Rotation Period}}\)

Speed = \(\frac{36,000,000 \text{ m}}{72,000 \text{ s}}\)

Now, we perform the division:

Speed = \(\frac{36,000,000}{72,000} \text{ m/s}\)

Speed = \(\frac{36000}{72} \text{ m/s}\)

Speed = \(500 \text{ m/s}\)

Therefore, the speed of a point on the planet's equator is 500 m/s.

Revision Table: Planet Rotation Speed Calculation

Additional Information: Understanding Equatorial Speed

The speed calculated here is the linear speed of a point on the equator due to the planet's rotation. Points at different latitudes on the planet will have different linear speeds. Points closer to the poles travel a smaller distance during one rotation, so their linear speed is lower. The poles themselves, if they are the axis of rotation, have a linear speed of zero (though they complete a full rotation in terms of angle).

The formula used, Speed = Distance / Time, is a fundamental concept in physics for calculating average speed. In this case, because the point is moving in a circle at a constant rate, this is also its instantaneous speed.

Understanding unit conversions (like km to m and hours to seconds) is crucial for solving physics problems accurately. Always ensure all quantities are in consistent units before performing calculations.