Question

The Gravitron is a circular carnival ride that is 6.2m in radius and spins at a high rate of speed in order to simulate gravity. What velocity is required to experience an acceleration equal to Earth's gravity (aka 1g)?

If the velocity were 2 times faster, how many g's would the riders feel?

How would the radius need to change to allow the riders to experience 5g's at this new velocity?

Answer 1

The Gravitron is a circular carnival ride that is 6.2m in radius and spins at a high rate of speed in order to simulate gravity. What velocity is required to experience an acceleration equal to Earth's gravity (aka 1g)?

If the velocity were 2 times faster, how many g's would the riders feel?

How would the radius need to change to allow the riders to experience 5g's at this new velocity?

Solution:

The centripetal acceleration is:

$$a = \frac {v ^ {2}}{r}, \text{ were } v - \text{angular velocity}, r - \text{radius}$$

Such as $g = 9.8 \, ms^2$,

$$v = \sqrt{9.8r}$$ $$v = \sqrt{9.8 * 6.2} = 7.79 \, \text{radian/s}$$

If the velocity were 2 times faster: $a = g * 2^2 = 4g$

In order to make acceleration 5g the radius must be: $R = \frac{5}{4} R_0$, $R = 7.75 \, m$