Question

The wheel starting from rest is rotating with a constant angular acceleration $3rad/s^2$, the radius of wheel is $0.5m$. The centripetal acceleration of the particle on the rim at end of $2$ seconds is

• A. $10m/s^2$
• B. $15m/s^2$
• C. $18m/s^2$
• D. $12m/s^2$

Answer 1

The correct option is C $18m/s^2$

Given that a wheel is rotating with constant angular acceleration $=\alpha =3rad/s^2$

Radius of wheel is $=r=0.5m$

Angular velocity of wheel at any time $t$ =$\omega ={\omega }_o+\alpha t$

$⟹\omega =3t$

at $t=2secs$

$⟹\omega =6rad/s$

$\therefore$ Centripetal acceleration of the particle at $t=2sec⟹a_c={\omega }^{2}r$

$⟹a_c=6^2\ast 0.5=18m/s^2$