Question

A linear force 25n is applied to the of uniform disc parallel to its plane . If radius is 20cm and mass 30kg ,then angular displacement produced in 12 seconds is

Answer 1

$\Large\boxed{\sf{\quad298.8\ rad\quad}}$

Given,

• $\sf{F=25\ N}$

• $\sf{r=0.2\ m}$

• $\sf{m=30\ kg}$

• $\sf{t=12\ s}$

Assume the disc rotates from rest, then its initial angular velocity is zero.

• $\sf{\omega_0=0\ rad\ s^{-1}}$

The linear acceleration produced by the force on the disc is,

$\longrightarrow\sf{a=\dfrac{F}{m}}$

$\longrightarrow\sf{a=\dfrac{25}{30}}$

$\longrightarrow\sf{a=0.83\ m\ s^{-2}}$

And the angular acceleration produced is,

$\longrightarrow\sf{\alpha=\dfrac{a}{r}}$

$\longrightarrow\sf{\alpha=\dfrac{0.83}{0.2}}$

$\longrightarrow\sf{\alpha=4.15\ rad\ s^{-2}}}$

Then the angular displacement produced is given by,

$\longrightarrow\sf{\theta=\omega_0 t+\dfrac{1}{2}\alpha t^2}$

$\longrightarrow\sf{\theta=0\times12+\dfrac{1}{2}\times4.15\times12^2}$

$\longrightarrow\sf{\underline{\underline{\theta=298.8\ rad}}}$