Question

An old wheat-grinding wheel in a museum actually works. The sign on the wall says that the wheel has a rotational acceleration of 210 rad/s^2 as it's spinning rotational speed increases from zero to 1900 rpm. How long does it take the wheel to attain this rotational speed?

Answer 1

Rotational acceleration of the wheel is, $\alpha$ = 210 rad/s²

Initial spinning rotational speed of the wheel is, $\omega _{i}$ = 0 rpm

1 rpm = (1/60) revolution per second = 2$\pi$ * (1/60) rad/s

Thus,

$\omega _{i}$ = 0 rad/s

Final spinning rotational speed of the wheel is, $\omega _{f}$ = 1900 rpm = 198.99 rad/s

Now, from the equations of motion (for rotational motions),

$\omega _{f}$ = $\omega _{i}$ + $\alpha$ t

where t is the time taken by the wheel to attain its final rotational speed.

198.99 = 0 + 210 * t

t = 198.99 / 210

t = 0.947571429 s = 0.95 s