Total Angular Momentum of the Earth

Click For Summary
SUMMARY

The discussion focuses on calculating the total angular momentum of the Earth, specifically determining the period of rotation (T) required for this momentum to equal zero. The key equations involved are Ltot = Ltrans + Lrot, Lrot = Iw, and w = 2pi/T. Participants clarify that the angular momentum of the Earth in orbit should be treated as a point mass, leading to the equation mvr = Iw, where I is the moment of inertia. The conversation emphasizes the importance of correctly identifying variables and their meanings in the context of angular momentum calculations.

PREREQUISITES
  • Understanding of angular momentum concepts
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of circular motion and gravitational forces
  • Basic proficiency in algebraic manipulation of equations
NEXT STEPS
  • Study the derivation of angular momentum equations in classical mechanics
  • Learn about the moment of inertia for different shapes and masses
  • Explore the relationship between linear and angular velocity in circular motion
  • Investigate the effects of gravitational forces on orbital motion
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of planetary motion and angular momentum calculations.

v3r
Messages
5
Reaction score
0

Homework Statement


How long should the day be so that the total angular momentum of the Earth
(including its rotation about its own axis and its (approximately) circular orbit around the
sun) is zero (Note: the magnitude of the angular velocity is 2pi/T where T is the period of rotation?)

Homework Equations


Ltot = Ltrans + Lrot
Lrot = Iw^2
w = 2pi/T

The Attempt at a Solution


Ltot = 0

I am really clueless. I don't know where to start..
 
Physics news on Phys.org
v3r said:

Homework Statement


How long should the day be so that the total angular momentum of the Earth
(including its rotation about its own axis and its (approximately) circular orbit around the
sun) is zero (Note: the magnitude of the angular velocity is 2pi/T where T is the period of rotation?)

Homework Equations


Ltot = Ltrans + Lrot
Lrot = Iw^2
w = 2pi/T

The Attempt at a Solution


Ltot = 0

I am really clueless. I don't know where to start..

you're started. double check your equation
Lrot = Iw^2

There shouldn't be a square there. For the Earth's orbital angular momentum, just treat the Earth like a point mass at a distance r.

L=mvr
 
So it should be
Ltot = Ltrans + Lrot
Ltot = 0
Ltrans = Lrot
mvr = Iw
mvr = 2pi/T * I
mvr = 2pi/T * mr^2
v/r = 2pi/T

I'm still confused.
 
v3r said:
So it should be
Ltot = Ltrans + Lrot
Ltot = 0
Ltrans = Lrot
mvr = Iw
mvr = 2pi/T * I
mvr = 2pi/T * mr^2
v/r = 2pi/T

I'm still confused.

You're getting there. Remember, you're looking for the period of one day on Earth under your new conditions. what variable do you want to solve for?

Also, be carefull with your variables. You've used "r" to stand in for two different things.

What is the r in Ltrans = mvr?
What is the r in I = mr^2?
 
r in I would be the perpendicular distance which would be the radius of the earth.
r in Ltrans would be the distance to the center of mass which would be the distance of Earth from sun?

I want to solve for v in order to get the time by dividing it by the radius?
 
You're almost there. Now use another variable to re-name one of your r's. Eventually, you want to solve for period T. However, you have the Earth's orbital velocity v to get rid of. For this, use univorm circular motion, and universal gravitation.

F=m(v^2) / rF=GmM / (r^2)
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Angular Momentum Problem: Mouse walking on a rotating turntable
  • · Replies 5 ·
Replies
5
Views
1K
How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
  • · Replies 335 ·
12
Replies
335
Views
16K
Angular momentum conservation on a merry-go-round
  • · Replies 5 ·
Replies
5
Views
2K
Perfectly inelastic collision between Projectile and a hinged disk
  • · Replies 26 ·
Replies
26
Views
1K
Conservation of angular momentum
  • · Replies 2 ·
Replies
2
Views
2K
Angular momentum of a rotating disc
  • · Replies 3 ·
Replies
3
Views
2K
How Does Earth Maintain Its Angular Momentum After the Sun Disappears?
  • · Replies 7 ·
Replies
7
Views
2K
Clarification on angular momentum
  • · Replies 1 ·
Replies
1
Views
2K
Kepler's Third Law vs Conservation of angular momentum
  • · Replies 8 ·
Replies
8
Views
2K
Conservation of angular momentum
  • · Replies 22 ·
Replies
22
Views
4K