Question

Find the angular velocity of a satellite which revolves in a circular orbit of radius 35000 km and completes one round in 12 hours.

Answer 1

Given Conditions ⇒

Radius of the circular orbit = 35,000 km.

Time taken to complete one round = 12 hours.

Angle subtended at the centre = 360° [ ∵ Earth is approx circular].
∵ 360° = 2π rad.
∴ Angle subtended at the centre = 2π


Now, Using the Formula,

Angular Velocity (ω) = Angle subtended at the centre in radians/Time taken to complete 1 round.

∴ ω = 2π/12
⇒ ω =(44/7) ÷ 12
⇒ ω = 0.524 rad/hr.

∴ Angular velocity of the satellite is 0.524 rad/hr.


Hope it helps.

Answer 2

In the attachment I have answered this problem.

I have applied basic the relation

Linear velocity
= Angular velocity × radius

to solve this problem.

See the attachment for detailed solution .