Answer :
Explanation:
Given that,
Initial speed, u = 0
No of rotation is 1 in every 1.2 s
The astronaut is strapped into a seat 4.00 m from the axis, r = 4 m
(a) Let [tex]\alpha[/tex] is the angular acceleration during the first 40 s. It is given by :
[tex]\alpha =\dfrac{\omega}{t}[/tex]
[tex]\omega=\dfrac{2\pi r}{t}[/tex]
[tex]\omega=\dfrac{2\pi }{1.1}[/tex]
[tex]\omega=5.71\ rad/s[/tex]
[tex]\alpha =\dfrac{5.71}{40}[/tex]
[tex]\alpha =0.142\ rad/s^2[/tex]
Tangential acceleration is given by :
[tex]a=r\times \alpha[/tex]
[tex]a=4\times 0.142[/tex]
[tex]a=0.568\ m/s^2[/tex]
(b) Let a is the centripetal acceleration. It is given by :
[tex]a=\omega^2r[/tex]
[tex]a=5.71^2\times 4[/tex]
[tex]a=130.41\ m/s^2[/tex]
Since, [tex]g=9.8\ m/s^2[/tex]
[tex]a=13.3\ g[/tex]
Hence, this is the required solution.