Answer:
[tex]w^2=5.5rads/s[/tex]
Explanation:
From the question we are told that:
Mass [tex]m=2.0kg[/tex]
Radius [tex]r=1.8m[/tex]
Height [tex]h=7.5m[/tex]
Generally the equation for Potential energy is mathematically given by
Potential energy=Kinetic energy+Rotational energy
[tex]mgh=\frac{1}{2}mv^2+\frac{1}{2}Iw^2[/tex]
Since there is no slipping
[tex]v=rw[/tex]
Therefore
[tex]mgh=\frac{1}{2}mr^2w^2+\frac{1}{2}Iw^2[/tex]
Where
[tex]I=\frac{1}{2}mr^2[/tex]
[tex]l=3.24m[/tex]
[tex]2*9.81*7.5=\frac{1}{2}(2)(1.8)^2w^2+\frac{1}{2}(3.24)w^2\\\\[/tex]
[tex]147.15=3.24w^2+1.62w^2[/tex]
[tex]w^2=\frac{147.15}{4.86}[/tex]
[tex]w^2=\sqrt{\frac{147.15}{4.86}}[/tex]
[tex]w^2=5.5rads/s[/tex]
