# Thread: [SOLVED] Radian Measure and Angular Velocity

1. ## [SOLVED] Radian Measure and Angular Velocity

Assalamu Alaikum Wa Rahmatullah Wa Barakatuh I am lost!

An object has a circular orbit with a 0.05 radians per sec. angular velocity

- how long for 1 orbit?
- whats the speed if it orbits at 550 kmph above earth with a 6000 km radius

2. Originally Posted by -DQ-
Assalamu Alaikum Wa Rahmatullah Wa Barakatuh I am lost!

An object has a circular orbit with a 0.05 radians per sec. angular velocity

- how long for 1 orbit?
- whats the speed if it orbits at 550 kmph above earth with a 6000 km radius

It travels 0.05 radians a second, and there are $\displaystyle 2 \pi$ radians in an orbit. So the time for one orbit is $\displaystyle \frac{2\pi}{0.05}$ seconds.

If it's speed is 550kmph and its distance to travel is 6000km, then it takes $\displaystyle \frac{6000}{550}$ hours to cover that speed. Which is $\displaystyle \frac{6000}{500 \times 60 \times 60}$ seconds!

So we now know how long it takes to complete and orbit, and we know an orbit is still 2pi radians!

So it's angular velocity is $\displaystyle \frac{2 \pi}{\frac{6000}{500 \times 60 \times 60}}$ radians per second!

3. Jazakallah Kkair!

Thanks so much for the quick help!