Question

A particle moving in a circle changes its angular velocity uniformly from $20\text{rad/s}$ to $40\text{rad/s}$ in first 5 seconds. Find the angular acceleration of the particle.

• A. $4{\text{rad/s}}^2$
• B. $2{\text{rad/s}}^2$
• C. $2.5{\text{rad/s}}^2$
• D. $3{\text{rad/s}}^2$

Answer 1

The correct option is A $4{\text{rad/s}}^2$

It is given that the angular velocity uniformly changes from $20\text{rad/s}$ to $40\text{rad/s}$ in $5s$

By the equation of motion having constant angular acceleration $\left(\alpha \right)$ we know that,

$\omega ={\omega }_0+\alpha t$,

Given ${\omega }_0=20\text{rad/s}$ is the initial angular velocity,
$\omega =40\text{rad/s}$, is the final angular velocity and
$t=5s$.

We get the angular acceleration as,
$\alpha =\frac{40-20}{5}=4{\text{rad/s}}^2$

Option A is the correct answer.