Compute the angular momentum of the earth arising from the following motions.
(a) Earth's orbital motion around the sun.
(b) Earth's rotation on its axis.
also include the units please. im not sure if i have the right answer because the site tells me my units are wrong, so for all i know i have the right answer but i cant tell
ok that's correct
To compute the angular momentum of the Earth arising from its motions, we need to consider two components: (a) Earth's orbital motion around the sun and (b) Earth's rotation on its axis.
(a) Earth's orbital motion around the sun:
The angular momentum of an object in circular motion is given by the product of its moment of inertia and angular velocity. In the case of Earth's orbital motion, we can consider the Earth as a point mass revolving around the sun.
To calculate the angular momentum, we need to know the moment of inertia and the angular velocity. The moment of inertia of a point mass is given by I = m * r^2, where m is the mass and r is the distance from the axis of rotation. However, Earth's moment of inertia is not relevant here since we are considering the Earth as a point mass.
The angular velocity, ω, is equal to the rate of change of angle α with respect to time t, which is given by ω = dα/dt. For the Earth's orbital motion, the angular velocity is equal to the angular speed of the Earth around the sun, which is approximately 2π radians per year.
Therefore, the angular momentum of Earth's orbital motion around the sun is given by L = I * ω = m * r^2 * ω, where r is the average distance between the Earth and the sun.
(b) Earth's rotation on its axis:
The angular momentum of Earth's rotation on its axis can be calculated using a similar formula. However, in this case, we need to consider the moment of inertia of the Earth.
The moment of inertia of a rotating solid body is given by I = 2/5 * m * r^2, where m is the mass of the body and r is the radius of rotation. For the Earth, the moment of inertia around its axis is approximately 8.04 * 10^37 kg * m^2.
The angular velocity, ω, for Earth's rotation is equal to the rate of change of angle θ with respect to time t, which is given by ω = dθ/dt. The angular velocity of Earth's rotation is approximately 2π radians per day.
Therefore, the angular momentum of Earth's rotation on its axis is given by L = I * ω = 2/5 * m * r^2 * ω.
To obtain the numerical values for the angular momenta, you would need to know the mass of the Earth and the average distance between the Earth and the sun.
(a) L1 = M•v•R =
Earth’s mass is M = 5.97•10^24 kg,
R= 1.5•10^11 m (Earth-Sun)
v=ω•R=2•π•n•R
n=1 rev/year =1/365•24•3600 rev/s
L1 = M•v•R = M•2πn•R²= …(kg•m²/s)
(b)
Earth’s radius is r = 6.378•10^6 m.
n= 1rev/day =1/24•3600 rev/s
L2 = I•ω1= (2•M•r²/5) •2•π•n•r= …(kg•m²/s)