Question

A particle, situated in an object, moves with angular acceleration of $6rad/{\sec }^2$ and with $2rad/\sec$ angular velocity. If the radius of the circular path is $1m$, its total acceleration in $m/{\sec }^2$ will be-

• A. $\sqrt{52}$
• B. $100$
• C. $10$
• D. $\sqrt{10}$

Answer 1

The correct option is A $\sqrt{52}$

We have

$a_n=w^{2}r={\left(2\right)}^2\left(1\right)=4m/s^2$

$a_t=xr=\left(6\right)\left(1\right)=6m/s^2$

$a_{net}=\sqrt{a{n}^2+a{t}^2}$

$=\sqrt{{\left(4\right)}^2+{\left(6\right)}^2}$

$=\sqrt{16+36}$

$=\sqrt{52}m/s^2$