Question #25b65

1 Answer
Feb 23, 2018

Answer:

Option (3) only if #omega_o=omega_s\ i.e.,#
Orbital angular velocity is equal to spin angular velocity.

Explanation:

Let the spherical satellite of mass #m# be spinning about an axis passing through its center with angular velocity #omega_s#.
Its spin angular momentum #L_s# is is given as

#L_s=Iomega#
where #I# is its moment of inertia and for a sphere #=2/5ma^2#

#:.L_s=2/5ma^2omega_s# .........(1)

Orbital angular momentum #vecL_o# of satellite, considered a point mass, revolving in a circle of radius #r# is given as the cross product of the position vector #vecr# and its linear momentum #vecp = m vecv#.

#vecL = vecr × vecp#

Let #omega_o# be orbital angular velocity. We have #v=bomega_o#.
Orbital velocity is always perpendicular to the radius vector hence #sin theta# of the cross product is #=1#, and #r=b#, we get

#L_o = b^2 momega_o# .........(2)

Ratio of orbital angular momentum to spin angular momentum is

#L_o/L_s=(b^2 momega_o)/(2/5ma^2omega_s)#
#L_o/L_s=(5b^2 omega_o)/(2a^2omega_s)#