Answer to Question #104291 in Classical Mechanics for Joshua

Question

Week 4

1. This artist's conception imagines a 'wheel-shaped' space station. The idea is that the 'wheel' would turn on its axis at a rate such that the acceleration in the rim of the wheel would be 9.8 m/s^2. (This would make inhabitants feel as though they had their normal weight.) Suppose that the radius of the wheel is 1.0 x 10^2 m. What is the required period of rotation of the space station about its axis? (Follow the significant number for the final answer).

Answer 1

As per the question,

Acceleration in the rim of the wheel is $(a)=9.8 m/sec^2$

Radius of the wheel (R)=$1.0 \times 10^2 m$

We know that $a=R\omega^2$

$\omega=$ angular velocity of the wheel

We know that angular velocity $(\omega)=\dfrac{2\pi}{T}$

where T is the time period.

So,

$9.8 m/sec^2=1.0\times \dfrac{2\pi}{T}$

$\Rightarrow T=\dfrac{2\pi}{9.8}=0.64 sec$

or 0.6 sec