Answer:
303.9481875 N
Explanation:
t = Time taken = 2 seconds
F = Force
r = Radius = 1.5 m
I = Moment of Inertia
[tex]\alpha[/tex] = Angular Acceleration
Torque
[tex]\tau=F\times r[/tex]
[tex]\tau=I\times \alpha[/tex]
[tex]\\\Rightarrow F\times r=I\times \alpha\\\Rightarrow F=\frac{I\times \alpha}{r}[/tex]
Angular velocity
[tex]\omega=rev/s\times 2\pi\\\Rightarrow \omega=0.6\times 2\pi\\\Rightarrow \omega=3.76991\ rad/s[/tex]
Angular acceleration
[tex]\alpha=\frac{\omega}{t}\\\Rightarrow \alpha=\frac{3.76991}{2}\\\Rightarrow \alpha=1.88495\ rad/s^2[/tex]
[tex]I=\frac{1}{2}mr^2\\\Rightarrow I=\frac{1}{2}215\times 1.5^2\\\Rightarrow I=241.875\ kgm^2[/tex]
[tex]F=\frac{I\times \alpha}{r}\\\Rightarrow F=\frac{241.875\times 1.88495}{1.5}\\\Rightarrow F=303.9481875\ N[/tex]
The magnitude of the force to stop the merry-go-round is 303.9481875 N
