The earth moves round the sun in one year.the average earth-sun distance is 1.5*10^11m given that the mass of the earth is 5.98*10^24kg
(a):the angular momentum of the earth???
(b):kinetic energy of the earth motion??
(c):kinetic energu of the earth motion half way along it axis???
Please help me it too difficult
a. Angular amomentum= mr^2*w
= M r^2*2PI/yearinseconds
b. KE=1/2 I w^2=1/2 Mr^2 (2PI/yearinsecons)^2
c. I am not certain what "its" axis refers to, but I think someone is wanting you to use the parallel axis theorm.
I'd be happy to help you with your questions! Let's break down each question and find the answers step by step:
(a) The formula for angular momentum is given by L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
To find the angular momentum of the Earth, we need to calculate the moment of inertia and the angular velocity.
The moment of inertia for a planet is given by I = 2/5 * m * r^2, where m is the mass of the planet and r is the distance from the rotation axis (in this case, the axis passing through the center of the Earth).
For the Earth, we are given the mass (m = 5.98*10^24 kg) and the average Earth-sun distance (r = 1.5*10^11 m). Plugging in these values:
I = 2/5 * (5.98*10^24 kg) * (1.5*10^11 m)^2
Now we need to calculate the angular velocity. The angular velocity, ω, is given by ω = 2π/T, where T is the period of revolution (in this case, 1 year or 365 days).
T = 365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 3.15 * 10^7 seconds
Plugging in this value, we can calculate ω.
ω = 2π / (3.15 * 10^7 seconds)
Once you have the values for I and ω, you can substitute them into the formula L = Iω to find the angular momentum of the Earth.
(b) The formula for the kinetic energy of motion is given by K = 1/2 * I * ω^2, where K is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
Using the values we calculated for I and ω in part (a), you can plug them into this formula to find the kinetic energy of the Earth's motion.
(c) To find the kinetic energy of the Earth's motion halfway along its axis, we need to consider the rotational kinetic energy. The formula for rotational kinetic energy is given by Krot = 1/2 * I * ω^2.
Since we're looking for the kinetic energy halfway along the Earth's axis, we need to consider the new moment of inertia. The moment of inertia is given by I = 1/2 * m * r^2, where m is the mass of the Earth and r is the distance from the axis of rotation (in this case, the radius of the Earth).
We already know the mass of the Earth (m = 5.98*10^24 kg), and the radius of the Earth is approximately 6.37*10^6 m.
Plugging in these values for I and ω into the formula Krot = 1/2 * I * ω^2, you can calculate the kinetic energy of the Earth's motion halfway along its axis.
I hope this explanation helps! Let me know if you have any further questions.