Question

A wheel starting with angular velocity of $10\text{rad/sec}$ acquires angular velocity of $100\text{rad/sec}$ in $15\text{seconds}$. If angular acceleration of wheel is constant, what will be the angular displacement of a point on the wheel in $15\text{seconds}$?

• A. $820\text{rad}$
• B. $825\text{rad}$
• C. $675\text{rad}$
• D. $150\text{rad}$

Answer 1

The correct option is B $825\text{rad}$

Given that, ${\omega }_o=10\text{rad/sec}$, ${\omega }_1=100\text{rad/sec}$, $t=15\text{sec}$

From equation of motion, we know that
${\omega }_1={\omega }_o+\alpha t$
So, $100=10+\alpha \times 15$
$\Rightarrow \alpha =6{\text{rad/sec}}^2$

Again, we know that,
$\theta ={\omega }_{o}t+\frac{1}{2}\alpha t^2$
$\therefore \theta =10\times 15+\frac{1}{2}\times 6\times {15}^2$
$\Rightarrow \theta =825\text{rad}$