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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.

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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


v=\omega\cdot(6371\operatorname{km})=(5559.74632m)/(s)

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)

User Adrian Regan
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