The 50 kg flywheel has a radius of gyration of 200 mm about

The 50 kg flywheel has a radius of gyration of 200 mm about its center of mass. It is subjected to a variable torque as shown. What is its angular velocity when it has rotated 5 revolutions starting from rest?

Solution

Given:-

Mass of the wheel =m = 50kg

Radius of gyration = r = 200 mm = 0.2 m

1) moment of inertia of the fly wheel is given by

I = m x r²= 50 x 0.2²= 2 kg-m²

2) Mean speed of the fly wheel N = N1 + N2 /2

Where N1= Maximum speed= 5 rev N2= minimum speed = 0 rev

N= 5+0/2 = 2.5 rev

Since enrgy stored in flywheel is given by,

E= 3.14²/900 x m x k² N x(N1-N2)=

3.14²/900 x 50 x 0.2² x 2.5 x 5= 0.2738 joules

Cs= coefficient of fluctuation of speed = N1 -N2 /N = 2

Energy stored = m x w² x r² x Cs

0.2738 = 2 x 2 x w²

w= 0.2616 Rad/sec.......ans