In my trigonometry class, we were assigned a problem on Angular and Linear Velocity.

Here's the excerpt:
This reflecting telescope is deployed in low-earth orbit (600km) with each orbit lasting 95min.
If the radius of the Earth is 6370km, what are the angular and linear velocity of the Hubble?

Please help, I don't know how to find the velocities for this problem and which formulas to use!

1) 0.0011 rad/s

2) 7667 m/s

Explanation:

1)

The angular velocity of an object in circular motion is equal to the rate of change of its angular position. Mathematically:

where

is the angular displacement of the object

t is the time elapsed

is the angular velocity

In this problem, the Hubble telescope completes an entire orbit in 95 minutes. The angle covered in one entire orbit is

rad

And the time taken is

Therefore, the angular velocity of the telescope is

2)

For an object in circular motion, the relationship between angular velocity and linear velocity is given by the equation

where

v is the linear velocity

is the angular velocity

r is the radius of the circular orbit

In this problem:

is the angular velocity of the Hubble telescope

The telescope is at an altitude of

h = 600 km

over the Earth's surface, which has a radius of

R = 6370 km

So the actual radius of the Hubble's orbit is

Therefore, the linear velocity of the telescope is:

their crystal patterns have been disrupted by stress