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