Question

A flywheel in the form of a uniformly thick disk of radius 1.33 m1.33 m has a mass of 70.6 kg70.6 kg and spins counterclockwise at 217 rpm217 rpm . Calculate the constant torque required to stop it in 2.75 min2.75 min .

Answer 1

Answer:

The constant torque required to stop the disk is 8.6 N-m in clockwise direction .

Explanation:

Let counterclockwise be positive direction and clockwise be negative direction .

Given

Radius of disk , r = 1.33 m

Mass of disc , m = 70.6 kg

Initial angular velocity , $\omega_i =217 rpm$

Final angular velocity , $\omega_f =0\, rpm$

Time taken to stop , t = 2.75 min

Let $\alpha$  be the angular acceleration

We know

$\omega _f=\omega _i+\alpha t$

=>$0=217+2.75\alpha =>\alpha = -78.9\frac{rev}{min^{2}}$

=>$\alpha =-\frac{78.9\times 2\pi}{60\times 60}\frac{rad}{s^{2}}=-0.138 \frac{rad}{s^{2}}$

Torque required to stop is given by

$\tau =I\alpha$

where  moment of inertia , $I=\frac{mr^{2}}{2}=\frac{70.6\times 1.33^{2}}{2}kg.m^{2}=62.5 kg.m^{2}$

=>$\therefore \tau =-0.138\times 62.5\, N.m=-8.6\, N.m$

Thus the constant torque required to stop the disk is 8.6 N-m in clockwise direction .