Question

A space research pod goes around the earths circumference in 2 hours. Find it’s angular velocity in radians per second and it’s linear speed in feet per minute and in miles per hour.

Answer 1

Let's find the angular velocity:

`\begin{gathered} \omega=2\pi f \\ f=(1)/(T) \\ \omega=(2\pi)/(T) \\ \omega=(2\pi)/(2)=(\pi rad)/(h) \end{gathered}`

We need to find the velocity in radians per second, so:

`\pi(rad)/(h)*(1h)/(3600s)=(\pi)/(3600)\approx(0.0008727rad)/(s)`

Let's find the linear speed:

`v=\omega\cdot r`

We need to express this speed in feet per minute, so:

`5559.746332(m)/(s)*(3,28084ft)/(1m)*(60s)/(1\min)=(1094438.289ft)/(\min )`

Now in miles per hour:

`1094438.289(ft)/(\min)*(1mi)/(5280ft)*(60\min )/(1h)=(12436.79874mi)/(h)`