Answer:
1) [tex]\alpha \approx 8.727\times 10^{-3}\,\frac{rad}{s^{2}}[/tex], 2) [tex]a_{r} = 14.222\,\frac{m}{s^{2}}[/tex], 3) [tex]a_{t} = 0.072\,\frac{m}{s^{2}}[/tex]
Explanation:
1) Let consider that Apollo spacecraft accelerates at constant rate. The angular acceleration of the spacecraft is:
[tex]\alpha = \left(\frac{1\,\frac{rev}{min} }{12\,min}\right)\cdot \left(\frac{2\pi\,rad}{1\,rev} \right)\cdot \left(\frac{1\,min}{60\,s} \right)[/tex]
[tex]\alpha \approx 8.727\times 10^{-3}\,\frac{rad}{s^{2}}[/tex]
2) The angular speed of the Apollo spacecraft at t = 2.5 min is:
[tex]\omega = \left(8.727\times 10^{-3}\,\frac{rad}{s^{2}} \right)\cdot (150\,s)[/tex]
[tex]\omega = 1.309\,\frac{rad}{s}[/tex]
The radial component of the linear acceleration is:
[tex]a_{r} = \left(1.309\,\frac{rad}{s}\right)^{2}\cdot (8.3\,m)[/tex]
[tex]a_{r} = 14.222\,\frac{m}{s^{2}}[/tex]
3) The tangential component of the linear acceleration is
[tex]a_{t} = \left(8.727\times 10^{-3}\,\frac{rad}{s}\right)\cdot (8.3\,m)[/tex]
[tex]a_{t} = 0.072\,\frac{m}{s^{2}}[/tex]
