for an 84 kg person standing at the equator what is the magnitude of angular momentum about the earths center due to earth's rotation
Earth’s radius is R = 6.378•10⁶ m.
L=Iω=mR²•2•π/24•3600=84•(6.378•10⁶)²•2• π/24•3600=….
What is the magnitude of angular momentum about the Earth's center of an 84kg person an equator due to the rotation of the Earth's
To calculate the magnitude of angular momentum about the earth's center due to the earth's rotation for an 84 kg person standing at the equator, you need to consider a few factors.
1. Determine the angular velocity (ω) of the earth's rotation at the equator. The earth completes one full rotation in approximately 24 hours, so the angular velocity can be calculated as:
ω = 2π / T
where T is the period of rotation in seconds.
T = 24 hours * 60 minutes * 60 seconds = 86400 seconds
ω = 2π / 86400 s
2. Calculate the orbital radius (r) at the equator. Earth's equatorial radius is approximately 6378.1 kilometers, so converting it to meters:
r = 6378.1 km * 1000 m/km
3. Determine the moment of inertia (I) of the person about the earth's axis of rotation. Assuming the person's mass is uniformly distributed, the moment of inertia can be calculated as:
I = 0.4 * m * r^2
where m is the mass of the person and r is the orbital radius.
m = 84 kg
I = 0.4 * 84 kg * (6378.1 km * 1000 m/km)^2
4. Finally, compute the magnitude of angular momentum (L) using the formula:
L = I * ω
L = (0.4 * 84 kg * (6378.1 km * 1000 m/km)^2) * (2π / 86400 s)
Calculating the above equation will give you the magnitude of angular momentum about the Earth's center.
To calculate the magnitude of the angular momentum about the Earth's center due to the Earth's rotation, we need to know the person's radius, as well as the Earth's mass and its rotational speed.
1. Earth's mass: The mass of the Earth can be found in scientific literature or online sources. Let's assume it is approximately 5.97 × 10^24 kg.
2. Earth's rotational speed: The Earth's rotational speed is usually given in terms of its angular velocity, which is the rate at which it rotates. The standard value for Earth's angular velocity is approximately 7.2921159 × 10^(-5) radians/second.
3. Radius of the person from the Earth's center: Since the person is standing at the equator, their radius from the Earth's center is equal to the Earth's radius, which is about 6,371 kilometers (or 6,371,000 meters).
Now, let's calculate the magnitude of the angular momentum using the following formula:
Angular Momentum = Moment of Inertia * Angular Velocity
The moment of inertia takes into account the distribution of mass, but for a simplified calculation, we can assume it is a point mass. The moment of inertia for a point mass rotating about an axis passing through its center of mass is given by:
Moment of Inertia = Mass * Radius^2
Plugging in the values, we get:
Moment of Inertia = 84 kg * (6,371,000 meters)^2
Finally, multiply the moment of inertia by the angular velocity to find the magnitude of the angular momentum:
Angular Momentum = Moment of Inertia * Angular Velocity
I will calculate the value for you.