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: http://zebu.uoregon.edu/1998/ph101/l16.html
Дата изменения: Tue Dec 1 20:23:37 1998 Дата индексирования: Tue Oct 2 01:07:46 2012 Кодировка: Поисковые слова: п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п |
Rotational Kinematics is very analagous to Linear Kinematics:
Linear Mechanics | Rotational Kinematics |
---|---|
Velocity | Angular Velocity |
Mass | Moment of Inertia |
Acceleration | Angular Acceleration |
Linear Momentum | Angular Momentum |
Angular velocity (w = number of rotations per second. One rotation is 360 degrees or 2p radians.
The total distance travelled in one rotation is:
2p R where R is the radius of the circle.
The orbital period, P, would be 2p R/V but P is just the inverse of the angular velocity w
So the linear velocity would be 2pR w or 2pR/P
Take the Earth:
Linear velocity at the surface is then:
2p(6000)/24 hours or around 1500 km/hr.
The earth-moon system is an interesting case of conservation of angular momentum.
The total angular momentum of the system is the sum of the rotational angular momentum of the earth and the moon and the orbital angular momentum of the moon.
The tidal force exerted by the moon on the earth is causing the rotation period of the earth to slow down. This loss in angular momentum of the system is not allowed and the only way in which the angular momentum can be constant is if the orbital angular momentum is increased.
This requires that the moon is getting farther away from the earth.
Orbital angular momentum = mass x orbital velocity x radius of orbit.
The orbital velocity of the moon depends only on its distance from the earth and the mass of the earth. As the radius increases the orbital velocity decreases but only as the square root of r. Thus increasing the radius increases the total orbital angular momentum.