Answer:
[tex]a=159.32\ m/s^2[/tex]
Explanation:
It is given that,
Angular speed of the football spiral, [tex]\omega=6.9\ rev/s=43.35\ rad/s[/tex]
Radius of a pro football, r = 8.5 cm = 0.085 m
The velocity is given by :
[tex]v=r\omega[/tex]
[tex]v=0.085\times 43.35[/tex]
v = 3.68 m/s
The centripetal acceleration is given by :
[tex]a=\dfrac{v^2}{r}[/tex]
[tex]a=\dfrac{(3.68)^2}{0.085}[/tex]
[tex]a=159.32\ m/s^2[/tex]
So, the centripetal acceleration of the laces on the football is [tex]159.32\ m/s^2[/tex]. Hence, this is the required solution.
