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Elliptical Orbits and Kepler's Laws

If the Earth ...

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If the Earth is treated as a sphere of radius r and mass m its angular momentum about the axis of its rotation with period t is

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Q. If the earth is treated as a sphere of radius

R

M

, its angular momentum about the axis of its rotation with period

T

Q. If the earth is treated as sphere of radius R and mass M, its angular momentum about the axis of its rotation with period T, is

Q. The angular momentum of a hollow sphere of radius R about an axis, passing through its centre of mass perpendicular to the plane and rotating with an angular velocity

ω

Q. The value of angular momentum of the earth rotating about its own axis is : (Mass of the earth=

5.978 \times 10^{24} k g

and Radius of earth=

6.378 \times 10^{6} m

)

Q. A uniform sphere of mass

m

r

and momentum of inertia

I

about its centre moves along the x-axis as shown in figure. Its centre of mass moves with velocity

= v_{0}

, and it rotates about its centre of mass with angular velocity

= ω_{0}

\to L = (I ω_{0} + m v_{0} r) (- k)

. The angular momentum of the body about the origin

O

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