Question

For a particle moving in a circle of radius $1\text{m}$, speed increases uniformly from $5\text{m/s}$ to $10\text{m/s}$ in $10\text{seconds}$. The value of angular acceleration of the particle is

• A. $50{\text{rad/s}}^2$
• B. $5{\text{rad/s}}^2$
• C. $0.5{\text{rad/s}}^2$
• D. $0.05{\text{rad/s}}^2$

Answer 1

The correct option is C $0.5{\text{rad/s}}^2$

Speed is increasing uniformly. Therefore, using 1st equation of motion,
$v=u+at$
$\Rightarrow a=\frac{v-u}{t}=\frac{10-5}{10}=0.5{\text{m/s}}^2$ is the linear acceleration.
Since, $a=r\alpha$, angular acceleration
$\alpha =\frac{a}{r}=\frac{0.5}{1}=0.5{\text{rad/s}}^2$