Question

 A fly wheel originally at rest is to reach an angular velocity of 42 rad/s in 7 s . Calculate the angular acceleration .



2 radian per second square

4 radian per second square

6 radian per second square

8 radian per second square

​

Answer 1

Given :

• Time taken by the fly wheel to reach an angular velocity of 42 rad/s = 7 sec

To Find :

• The angular acceleration of the fly wheel

Solution :

Now , by using first equation of motion in circular path ;

$\\ \star \: {\boxed{\red{\sf{ \omega_f = \omega_i + \alpha t}}}}$

Here ,

• $\sf{\omega_f}$ is final angular velocity
• ωᵢ is initial angular velocity
• α is angular acceleration
• t is time

We have ,

• $\sf{\omega_f}$ = 42 rad/s
• ωᵢ = 0 rad/s {Since we are given that the fly wheel is at rest}
• t = 7 sec

Substituting the values ;

$\\ : \implies \sf \: 42 \: rad .{s}^{ - 1} = 0 + \alpha(7 \: s)$

$\\ : \implies \sf \: 42 \: rad. {s}^{ - 1} = \alpha(7 \: s)$

$\\ : \implies \sf \alpha = \frac{42 \: rad. {s}^{ - 1} }{7 \: s}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{ \alpha = 6 \: \: rad. {s}^{ - 2} }}}}} \: \bigstar$

Hence ,

• The angular acceleration of the flywheel is 6 rad/s²

Answer 2

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

• A fly wheel originally at rest, i.e. initial angular velocity is zero.

• Final angular velocity is 42 rad/s.

$\Large\bf{\color{cyan}To\:FiNd,}$

• Angular acceleration of the wheel.

$\Large\bf{\color{lime}CaLcUlaTiOn,}$

$\bf\red{We\:know\:that}$

$\orange\bigstar\:\:\bf{\color{olive}\omega_f\:=\:\omega_i\:+\:\alpha{t}\:}$

$\bf\pink{Where,}$

• $\bf{\omega_f\:=\:Final\:angular\:velocity}$

• $\bf{\omega_i\:=\:Initial\:angular\:velocity}$

• $\bf{\alpha\:=\:angular\:acceleration}$

• t = Time period

$:\implies\:\:\bf{42\:=\:0\:+\:\alpha\times{7}\:}$

$:\implies\:\:\bf{\alpha\times{7}\:=\:42}$

$:\implies\:\:\bf{\alpha\:=\:\dfrac{42}{7}\:}$

$:\implies\:\:\bf\blue{\alpha\:=\:6\:rad/sec^2\:}$

$\Large\bold\therefore$ The angular acceleration of the wheel is $\bf\purple{6\:rad/sec^2}$.

$\green\bigstar\:\:{\boxed{\boxed{\color{coral}{\bf{Correct\:Option\:\longrightarrow\:(3)\:6\:rad/sec^2\:}}}}}$