Question

show time rate of angular momentum is Torque acting on a rotating body​

Answer 1

Answer:

To prove:

Rate of change of Angular Momentum is equal to Torque acting on the body.

Proof:

Let Moment of Inertia be I , angular Velocity be ω and Torque be τ and angular momentum be L

So we know that :

$angular \: momentum = I \times \omega$

$= > L \: = I \times \omega$

Now , Rate of change of Angular Momentum is as follows :

$\frac{dL}{dt} = \frac{d(I \times \omega)}{dt}$

$\frac{dL}{dt} = I \times \frac{d( \omega)}{dt}$

$\frac{dL}{dt} = I \times \alpha$

$\frac{dL}{dt} = \tau \: = torque$

$\boxed{ \blue{hence \: proved}}$

Answer 2

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$\rule{200}{1}$

$\small{\underline{\green{\sf{Solution :}}}}$

As we know that :

$\large \star {\boxed{\sf{L \: = \: I \omega}}}$

$\implies {\sf{\tau \: = \: \dfrac{dL}{dt}}}$

$\implies {\sf{\tau \: = \: I \dfrac{d \omega}{dt}}}$

$\implies {\sf{\tau \: = \: I(\alpha)}}$

$\implies {\boxed{\sf{\tau \: = \: I \alpha}}}$