Question

A wheel has an angular acceleration of $3.0\mathrm{rad}/{\mathrm{s}}^2$and an initial angular speed of $2.00\mathrm{rad}/\mathrm{s}$. In a time of $2\mathrm{s}$, it has rotated through an angle (in radian) of:

• A. $6$
• B. $12$
• C. $10$
• D. $4$

Answer 1

The correct option is C

$10$

Explanation for correct option:

Step 1: Given

Angular acceleration, $\mathrm{\alpha }=3\mathrm{rad}/{\mathrm{s}}^2$

Initial angular speed, ${\mathrm{\omega }}_0=2\mathrm{rad}/\mathrm{s}$

Time, $\mathrm{t}=2\mathrm{s}$

Step 2: Formula used

Angular displacement is given by,

$\mathrm{\theta }={\mathrm{\omega }}_0\mathrm{t}+\frac{1}{2}{\mathrm{\alpha t}}^2$

Step 3: Calculating the angle

Thus,

$\mathrm{\theta }=2\times 2+\frac{1}{2}\times 3\times 2^2$

$\mathrm{\theta }=4+6$

$\mathrm{\theta }=10$

The wheel is rotated at an angle of $10°$.

Therefore, the correct option is (C).