Question

Astronauts in the International Space Station must work out every day to counteract the effects of weightlessness. Researchers have investigated if riding a stationary bicycle while experiencing artificial gravity from a rotating platform gives any additional cardiovascular benefit. What frequency of rotation, in rpm, is required to give an acceleration of 1.4g to an astronaut's feet, if her feet are 1.1m from the platform's rotational axis?

Answer 1

Answer:

  33.725 rpm

Explanation:

The relationship between rotational speed in radians per second and acceleration is ...

  $\omega=\sqrt{\dfrac{a}{r}}$

We want the rotation rate in RPM, so we need the conversion ...

  $\text{RPM}=\dfrac{\text{rad}}{\text{s}}\cdot\dfrac{1\,\text{rev}}{2\pi\,\text{rad}}\cdot\dfrac{60\,\text{s}}{1\,\text{min}}$

Then the required rotational speed in RPM is ...

  $RPM=\sqrt{\dfrac{a}{r}}\cdot\dfrac{30}{\pi}=\dfrac{30}{\pi}\sqrt{\dfrac{1.4\cdot 9.8}{1.1}}\approx 33.725$

The rotation rate needs to be about 33.7 rpm to give an acceleration of 1.4g at the astronaut's feet.