Question

A wheel rotates with the constant acceleration of $2.0rad/s^2$, if the wheel starts from rest the number of revolution it makes in first ten seconds will be approximately

• A. 32
• B. 24
• C. 16
• D. 8

Answer 1

The correct option is C 16

For circular angular motion, the formula for angular displacement $\theta$ and angular acceleration $\alpha$ is
$\theta =\omega t+\frac{1}{2}\alpha t^{2}or\theta =0+\frac{1}{2}\alpha t^2$ where $\omega =$ initial velocity
or $\theta =\frac{1}{2}\times \left(2\right)(10{)}^2$
$\theta =100radians$
$2\pi$ radian are covered in 1 revolution.
$\therefore$ 1 radian is covered is covered in $\frac{1}{2\pi }$ revolution
or 100 radian are covered in $\frac{100}{2\pi }$ revolution.

$\therefore$ Number of revolution$=\frac{50}{3.14}=16$