Question

A flywheel in the form of a uniformly thick disk of radius 1.93 m has a mass of 92.1 kg and spins counterclockwise at 419 rpm. Calculate the constant torque required to stop it in 1.25 min.

Answer 1

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, $\omega_i=419\ rpm=43.87\ rad/s$

Final angular speed, $\omega_f=0$

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 :

$\tau=I\times \alpha$...........(1)

I is moment of inertia, for a solid disk, $I=\dfrac{mr^2}{2}$

$\alpha$ is angular acceleration

$I=\dfrac{92.1\ kg\times (1.93\ m)^2}{2}=171.53\ kgm^2$..............(2)

Now finding the value of angular acceleration as :

$\omega_f=\omega_i+\alpha t$

$0=43.87+\alpha \times 75$

$\alpha =-0.58\ m/s^2$..........(3)

Using equation (2) and (3), solve equation (1) as :

$\tau=171.53\ kgm^2\times -0.58\ m/s^2$

$\tau=-99.48\ N-m^2$

So, the torque require to stop the flywheel is 99.48 N-m². Hence, this is the required solution.