Question

In an engine governor, the two spheres (total mass of 1.0kg) are at 0.05m and rotating at 37rad/s If the engine increases the angular velocity to 58rad/s what is the new location of the spheres?

Answer 1

Here we can say that there is no external torque on this system

So here we can say that angular momentum is conserved

so here we will have

`I_1\omega_1 = I_2\omega_2`

now we have

`I_1 = mr^2`

`I_1 = (1kg)(0.05^2)`

`I_1 = 25* 10^(-4) kg m^2`

similarly let the final distance is "r"

so now we have

`I_2 = mr^2`

`I_2 = 1r^2`

now from above equation we have

`(25* 10^(-4))37 = (r^2)(58)`

`r = 0.04 m`

so final distance is 0.04 m between them