Chapter 12, Problem 8PS

(a)

To determine

To prove: The acceleration vector is $a=\left[\frac{d^{2}r}{d{t}^2}-r{\left(\frac{d\theta }{dt}\right)}^2\right]u_r+\left[r\frac{d^2\theta }{d{t}^2}+2\frac{dr}{dt}\frac{d\theta }{dt}\right]u_{\theta }$ where $u_r=\cos \theta i+\sin \theta j$ and $u_{\theta }=-\sin \theta i+\cos \theta j$ when the distance travelled by satellite in a circular motion around Earth is $42,000$ kilometers and the angular speed $\omega$ is $\frac{d\theta }{dt}=\frac{\pi }{12}\text{ radian per hour}$.

(b)

To determine

To calculate: The radial and angular component of the acceleration when the distance travelled by satellite in a circular motion around Earth is $42,000$ kilometers and the angular speed $\omega$ is $\frac{d\theta }{dt}=\frac{\pi }{12}\text{ radian per hour}$.