Question

the angular velocity of a wheel increases from 1200 to 4500 revolutions per minute in 10 second find its angular acceleration

Answer 1

$\Large\bf{\color{indigo}GiVeN,}$

Initial angular velocity $\bf{(\omega_1)}$ = 1200 rev/min = $\bf{\dfrac{1200}{60}\:=\:20\:rev/sec\:}$

Final angular velocity $\bf{(\omega_2)}$ = 4500 rev/min = $\bf{\dfrac{4500}{60}\:=\:75\:rev/sec\:}$

Time period = 10 sec

$\bf\pink{We\:know\:that,}$

$\red\bigstar\:\:\bf{\color{coral}\omega_2\:=\:\omega_1\:+\:\alpha{t}\:}$

$:\implies\:\:\bf{\alpha{t}\:=\:\omega_2\:-\:\omega_1\:}$

$:\implies\:\:\bf{\alpha\:=\:\dfrac{\omega_2\:-\:\omega_1}{t}\:}$

$\bf\red{Where,}$

$\bf\blue{\alpha\:=\:Angular\:acceleration\:}$

$:\implies\:\:\bf{\alpha\:=\:\dfrac{75\:-\:20}{10}\:}$

$:\implies\:\:\bf{\alpha\:=\:\dfrac{55}{10}\:}$

$:\implies\:\:\bf\green{\alpha\:=\:5.5\:rev/sec^2\:}$

$\Large\bold\therefore$ Angular acceleration of the wheel is $\bf\purple{5.5\:rev/sec^2\:}$.