Question

$\huge\orange{Solve\:It:-}$


A flywheel rotates with a uniform Angular acceleration .Its Angular Velocity increase from 20π rad/s to
40π rad/s in 10 sec. How many rotation did it made in this period .


​

Answer 1

$\huge\underline\green{\sf Answer}$

$\large{\boxed{\sf No.\:Of\:Rotation=150}}$

$\huge\underline\green{\sf Solution:-}$

Given :-

$\sf{\omega_{1}=20π rad/s}$

$\sf{\omega_{2}=40π rad/s}$

Time(t) = 10sec

No.Of Rotation = ?

$\large{\sf \omega_{2}=\omega_{1}+\alpha t}$

$\large{\sf 40π = 20π +10{\alpha}}$

$\large{\boxed{{\alpha = 2π rad/{s}^{2}}}}$

$\large{\boxed{\sf Angular\: Displacement \theta = {\frac{{\omega_{2}^{2} -{\omega_{1}^{2}}}}{2{\alpha}}}}}$

$\large\implies{\sf {\frac{{(40π)}^{2}-{(20π)}^{2}}{2×2π}}}$

$\large\implies{\sf ={\frac{{1200π}^{2}}{4π}}}$

$\large{\sf {\theta}=300π}$

THEREFORE NUNBER OF ROTATION :-

$\large{\boxed{\sf No.\:Of\:Rotation={\frac{{\theta}}{2π}}}}$

$\large\implies{\sf {\frac{300π}{2π}}}$

$\large{\boxed{\sf No.\:Of\:Rotation=150}}$

Answer 2

Refer to the Attachment ✌️