A fly wheel of moment of inertia I is rotatin | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Lets consider,

$n =$ initial frequency

$\omega=2 \pi n$

Initial kinetic energy is

$K _{ i }=\frac{1}{2} I \omega^2=\frac{1}{2} I 	imes 2

Vedclass · Accepted Answer

$6{\pi ^2}I{n^2}$

Vedclass · Answer

Lets consider,

$n =$ initial frequency

$\omega=2 \pi n$

Initial kinetic energy is

$K _{ i }=\frac{1}{2} I \omega^2=\frac{1}{2} I 	imes 2 \pi n 	imes 2 \pi n$

$K _{ i }=2 I \pi^2 n ^2$

When frequency is double to the initial frequency, the the kinetic energy will be

$K _{ f }=\frac{1}{2} I \omega^2=\frac{1}{2} I 	imes 4 \pi n 	imes 4 \pi n$

$K _{ f }=8 I \pi^2 n ^2$

By work-energy theorem,

$W = K _{ f }- K _{ i }$

$W =8 I \pi^2 n ^2-2 I \pi^2 n ^2=6 I \pi^2 n ^2$

A fly wheel of moment of inertia $I$ is rotating at $n$ revolutions per $sec$. The work needed to double the frequency would be

Similar Questions

If a solid sphere of mass $1\, kg$ and radius $0.1\, m$ rolls without slipping at a uniform velocity of $1\, m/s$ along a straight line on a horizontal floor, the kinetic energy is

A solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is ...

A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega$. Its centre of mass will rise upto maximum height :-

If a body completes one revolution in $\pi $ $sec$ then the moment of inertia would be