Question

please solve this with the solution ​

Answer 1

Answer:

Given:

Mass = 10^(-3) kg

Radius = 10 cm

Initial angular Velocity = 4π rad/s

Force acting = 10^(-4)π N

Time = 5 sec.

To find:

Angular Velocity at the end of 5 seconds

Calculation:

Linear acceleration is given by ratio of Force and mass.

$\therefore \: acc. = \dfrac{force}{mass}$

$\implies \: acc. = \dfrac{ ({10}^{ - 4} )\pi }{ {10}^{ - 3} }$

$\implies \: acc. = (0.1)\pi \: m {s}^{ - 2}$

Angular acceleration is given as :

$\boxed{acc. = r \times \alpha }$

$\implies \: (0.1)\pi = \dfrac{10}{100} \times \alpha$

$\implies \: \alpha = (\pi) \: rad \: {s}^{ - 2}$

Now , Final angular velocity is given as :

$\boxed{\omega 2 = \omega 1 + \alpha t}$

$\implies \: \omega2 = 4\pi + (\pi \times 5)$

$\implies \: \omega2 = (9\pi) \: rad \: {s}^{ - 1}$

So final answer :

$\boxed{ \sf{ \huge{ \red{ \: \omega2 = (9\pi) \: rad \: {s}^{ - 1}}}}}$

Answer 2

$\huge{\underline{\underline{\mathcal\green{\boxed{\boxed{SOLUTION\::}}}}}}$

$\implies$ $\sf{First \:calculate, \:linear \:acc.}$

$\implies$ $\sf{ a = f/m}$

$\implies$ $\sf{ a = 10-4π /10-^3}$

$\implies$ $\red{\boxed{a = (0.1)πms-2}}$

$\implies$ $\sf{now, \:calculate \:angular\: acceleration.}$

$\implies$ $\sf{acc. = r × α}$

$\implies$ $\sf{(0.1)π = 10/100 × α}$

$\implies$ $\green{\boxed{α = π \:rad \:s^-2}}$

$\implies$ $\sf{Now, \:calculate \:Angular\: velocity. }$

$\implies$ $\purple{w2= w1 +αt}$

$\implies$ $\sf{w2 = 4π + (π × 5)}$

$\implies$ $\large\blue{\boxed{\boxed{w2 = 9π rad s^-1}}}$