A 300 kg merry-go-round in the shape of a horizontal disk with a radius of 1.9 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. How large a torque would have to be exerted to bring the merry-go-round from rest to an angular speed of 3.6 rad/s in 3.5 s

Respuesta :

Answer:

557.7Nm

Explanation:

We are given that

[tex]m=300 kg[/tex]

Radius,r=1.9 m

Angular speed,[tex]\omega=3.6rad/s[/tex]

Time,t=3.5 s

Initial angular velocity,[tex]\omega_0=0[/tex]

We have to find the large torque would have to be exerted .

[tex]\alpha=\frac{\omega-\omega_0}{t}=\frac{3.6-0}{3.5}=1.03rad/s^2[/tex]

[tex]\tau=I\alpha[/tex]

[tex]\tau=\frac{1}{2}mr^2\alpha[/tex]

Where [tex]I=\frac{1}{2}mr^2[/tex]

Substitute the values

[tex]\tau=\frac{1}{2}(300)(1.9)^2(1.03)=557.7Nm[/tex]