Answer:
11.3m/s
Explanation:
We can find the solution through the rotational motion of the discus,
[tex]\theta = w_it+\frac{1}{2}\alpha t^2[/tex]
Where,
[tex]\theta = 2\pi[/tex]
[tex]w_i=0[/tex]
[tex]t=1s[/tex]
Solving to find [tex]\alpha[/tex],
[tex]2\pi = (0)(1)+\frac{1}{2}\alpha (1)^2[/tex]
[tex]\alpha = \frac{2\pi}{0.5}[/tex]
[tex]\alpha = 12.6 rad/s^2[/tex]
Therefore we can find the final angular velocity, through the rotational motion equation given by,
[tex]w_f = w_i + \alpha t[/tex]
Substituting,
[tex]w_f = 0 + 12.6*(1)[/tex]
[tex]w_f =12.6rad/s[/tex]
The diameter of the circle is 1.8m, then the ratio will be the half, i.e,
[tex]r=0.9m[/tex]
The relation between linear velocity and angular velocity is
[tex]v=rw_f[/tex]
[tex]v=(0.9)(12.6)[/tex]
[tex]v=11.3m/s[/tex]
