Question

A disc of radius $2cm$ rotating uniformly about a stationary axis with an angular velocity of $10rad/s$ is now experiencing an angular retardation of $\alpha =0.2t$. The magnitude of centripetal acceleration at $t=2s$ is

• A. $184cm/s^2$
• B. $200cm/s^2$
• C. $196cm/s^2$
• D. $216cm/s^2$

Answer 1

The correct option is A $184cm/s^2$

Given, $\alpha =0.2t$
$-\frac{d\omega }{dt}=0.2t$ (angular retardation)
$d\omega =-0.2tdt$
Integrating on both sides
${\int }_{{\omega }_0}^{\omega }d\omega =-{\int }_0^{2}0.2tdt$
$\omega -{\omega }_0=-0.2\frac{t^2}{2}{|}_0^2$
$\omega ={\omega }_0-0.1(2{)}^2$
$=10-0.4=9.6rad/s$
$\therefore$ centripetal acceleration $a_C=r{w}^2=2\times {10}^{-2}\times (9.6{)}^2$
$=1.84m/s^2=184cm/s^2$