Respuesta :
Answer:
Torque = 99.48 N-m²
Explanation:
It is given that,
Radius of the flywheel, r = 1.93 m
Mass of the disk, m = 92.1 kg
Initial angular velocity, [tex]\omega_i=419\ rpm=43.87\ rad/s[/tex]
Final angular speed, [tex]\omega_f=0[/tex]
We need to find the constant torque required to stop it in 1.25 min, t = 1.25 minutes = 75 seconds
Torque is given by :
[tex]\tau=I\times \alpha[/tex]...........(1)
I is moment of inertia, for a solid disk, [tex]I=\dfrac{mr^2}{2}[/tex]
[tex]\alpha[/tex] is angular acceleration
[tex]I=\dfrac{92.1\ kg\times (1.93\ m)^2}{2}=171.53\ kgm^2[/tex]..............(2)
Now finding the value of angular acceleration as :
[tex]\omega_f=\omega_i+\alpha t[/tex]
[tex]0=43.87+\alpha \times 75[/tex]
[tex]\alpha =-0.58\ m/s^2[/tex]..........(3)
Using equation (2) and (3), solve equation (1) as :
[tex]\tau=171.53\ kgm^2\times -0.58\ m/s^2[/tex]
[tex]\tau=-99.48\ N-m^2[/tex]
So, the torque require to stop the flywheel is 99.48 N-m². Hence, this is the required solution.
