Problem 4-62 Centripetal acceleration - B

An astronaut in training is spinning around in a device that rotates at 30 revolutions per minute. (a) If the astronaut is \(7.5\; m\) from the centre of the device, what is the magnitude of the centripetal acceleration? (b) Express the answer in terms of "\(g,\)" the magnitude of the acceleration due to gravity.
[Ans. (a) \(74\; m/s^2\)   (b) \(7.6\; g\)]

Accumulated Solution

The expression for centripetal acceleration is:  \( a_c = 4\pi ^2r/T^2\)

Correct!

\(a_c = v^2/r\)

Text Eq. 4-16.

In fact, the other choice \(a_c = 4\pi ^2r/T^2\) is also correct. We will use \(a_c = v^2/r\) but at the end you should go back and follow the alternate solution as well.

For this solution we need the value of \(T\) which is:

(A)   the time for one revolution

(B)   the time for 30 revolutions

(C)   the number of revolutions in one second