Question

A wheel rotates with a constant acceleration of 2.0 $\frac{rad}{s^2}$. If the wheel starts from rest, how many revolutions will it make in the first 10 seconds?

• A. 32
• B. 8
• C. 16
• D. 4

Answer 1

The correct option is C

16

The angular displacement in the first 10 seconds is given by

$\theta$ = ${\omega }_{0}t+\frac{1}{2}a{t}^2$ = $\frac{1}{2}\left(2.0\frac{rad}{s^2}\right)(10s{)}^2$ = 100 rad.

As the wheel turns by $2\pi$ radian inj each revolution, the number of revolutions in $10s$ is

$n$ = $\frac{100}{2\pi }$ $\approx$ 16.