Earth is spinning at 1670 km/h at the equator. Use this
number to find Earth’s equatorial diameter.
The final answer should be around 12,764 if you use 3.14 for pi. Circumference= diameter times pi. Take 1,670 times 24 to get circumference 40,080. Divide 40,080 by pi 3.14 whatever to get 12,764.
24 hr in a day
one revolution per day
1670 km is 1/24 of the equatorial circumference
To find Earth's equatorial diameter using the information that it is spinning at 1670 km/h at the equator, we can follow these steps:
Step 1: Convert the speed from km/h to m/s.
1 km = 1000 m
1 h = 3600 s
So, 1670 km/h = 1670 * 1000 m / 3600 s = 1670000 m / 3600 s = 463.89 m/s (approximately)
Step 2: Use the formula for linear velocity to find the equatorial diameter.
The formula for linear velocity (v) is given by:
v = ω * r
Where:
- v is the linear velocity,
- ω is the angular velocity (angular speed),
- r is the radius of the circular path.
The Earth's linear velocity (v) is equal to 463.89 m/s (approximately) since it is spinning at that speed.
The angular velocity (ω) can be calculated using the formula:
ω = 2π / T
Where:
- ω is the angular velocity,
- T is the period of rotation.
The period of rotation for the Earth is approximately 24 hours = 24 * 60 * 60 s = 86400 s.
Using the formula, we can calculate ω:
ω = 2π / 86400 s ≈ 7.272 × 10^(-5) rad/s (approximately)
Finally, we can rearrange the formula v = ω * r to find the radius (r):
r = v / ω
r ≈ 463.89 m/s / 7.272 × 10^(-5) rad/s ≈ 6374468.9 m (approximately)
The radius (r) is approximately 6374468.9 m.
Step 3: Calculate the equatorial diameter using the relationship between radius and diameter.
The diameter (d) is twice the radius:
d = 2 * r
d ≈ 2 * 6374468.9 m ≈ 12748937.8 m (approximately)
The equatorial diameter of Earth is approximately 12748937.8 meters.
To find Earth's equatorial diameter using the information about its rotation speed, it is necessary to apply some mathematical calculations. Let's break down the process step by step:
Step 1: Convert the given speed from km/h to meters per second (m/s):
To do this, we need to divide the given speed by 3.6 since there are 3.6 seconds in one hour.
1670 km/h ÷ 3.6 = 463.9 m/s (rounded to one decimal place)
Step 2: Calculate Earth's circumferential speed at the equator:
The circumferential speed at the equator can be found using the formula:
Circumferential speed = 2πr,
where r is the radius of the Earth and π is a mathematical constant approximately equal to 3.14159.
To isolate r, we can rearrange the formula to:
r = Circumferential speed ÷ (2π)
Substituting the given circumferential speed:
r = 463.9 m/s ÷ (2 × 3.14159) = 73.87 meters (rounded to two decimal places)
Step 3: Calculate Earth's equatorial diameter:
The equatorial diameter is the twice the radius of Earth since the radius represents the distance from the center to the edge. Thus, by multiplying the radius by 2, the equatorial diameter can be calculated as follows:
Equatorial diameter = 2 × r = 2 × 73.87 meters = 147.74 meters (rounded to two decimal places)
Therefore, the Earth's equatorial diameter based on the given rotation speed is approximately 147.74 meters.